From 37e6b33b5ba84285faab685a9008b9624569d805 Mon Sep 17 00:00:00 2001 From: Dan Sandiford Date: Mon, 28 Oct 2024 16:19:32 +1100 Subject: [PATCH] merge underworld-community material => model_code_inpuus --- model_code_inputs/.gitkeep | 1 - model_code_inputs/Dockerfile | 10 + model_code_inputs/Exp_A-3D.py | 455 +++++++++ model_code_inputs/Exp_B-2D.py | 770 +++++++++++++++ model_code_inputs/Exp_B-3D.py | 450 +++++++++ model_code_inputs/Exp_B_2D.ipynb | 931 ++++++++++++++++++ model_code_inputs/Exp_C-3D.py | 610 ++++++++++++ model_code_inputs/Exp_D-2D.py | 466 +++++++++ model_code_inputs/Exp_E-no-slip-version.py | 413 ++++++++ model_code_inputs/Exp_E_mixed-slip-version.py | 384 ++++++++ model_code_inputs/Exp_F-3D.py | 493 ++++++++++ model_code_inputs/README.md | 63 +- model_code_inputs/Results-all-simulations.zip | Bin 0 -> 624409 bytes model_code_inputs/Results_and_Figures.pdf | Bin 0 -> 2134762 bytes .../mesh_deform_default_swarm.png | Bin 0 -> 75801 bytes model_code_inputs/velocity_10000.0.png | Bin 0 -> 141643 bytes 16 files changed, 5043 insertions(+), 3 deletions(-) delete mode 100644 model_code_inputs/.gitkeep create mode 100644 model_code_inputs/Dockerfile create mode 100644 model_code_inputs/Exp_A-3D.py create mode 100644 model_code_inputs/Exp_B-2D.py create mode 100644 model_code_inputs/Exp_B-3D.py create mode 100644 model_code_inputs/Exp_B_2D.ipynb create mode 100644 model_code_inputs/Exp_C-3D.py create mode 100644 model_code_inputs/Exp_D-2D.py create mode 100644 model_code_inputs/Exp_E-no-slip-version.py create mode 100644 model_code_inputs/Exp_E_mixed-slip-version.py create mode 100644 model_code_inputs/Exp_F-3D.py create mode 100644 model_code_inputs/Results-all-simulations.zip create mode 100644 model_code_inputs/Results_and_Figures.pdf create mode 100644 model_code_inputs/mesh_deform_default_swarm.png create mode 100644 model_code_inputs/velocity_10000.0.png diff --git a/model_code_inputs/.gitkeep b/model_code_inputs/.gitkeep deleted file mode 100644 index 8b13789..0000000 --- a/model_code_inputs/.gitkeep +++ /dev/null @@ -1 +0,0 @@ - diff --git a/model_code_inputs/Dockerfile b/model_code_inputs/Dockerfile new file mode 100644 index 0000000..d29671c --- /dev/null +++ b/model_code_inputs/Dockerfile @@ -0,0 +1,10 @@ +FROM underworldcode/underworld2:2.12.2b + +# This command will copy in all the files in your repo. +COPY --chown=jovyan:users . /home/jovyan/community_model + +# Set working directory to where we've put files. +WORKDIR /home/jovyan/community_model + +# Create symbolic link to documentation. +RUN ln -s .. underworld_documentation diff --git a/model_code_inputs/Exp_A-3D.py b/model_code_inputs/Exp_A-3D.py new file mode 100644 index 0000000..d1ed55a --- /dev/null +++ b/model_code_inputs/Exp_A-3D.py @@ -0,0 +1,455 @@ +# --- +# jupyter: +# jupytext: +# formats: ipynb,md,py:light +# text_representation: +# extension: .py +# format_name: light +# format_version: '1.5' +# jupytext_version: 1.13.5 +# kernelspec: +# display_name: Python 3 (ipykernel) +# language: python +# name: python3 +# --- + +# This model is from Jan 2022. It contains important improvements over previous models, namely: +# +# - it doesn't need particles any more +# - (but still uses them in order to evaluate and visualize certain functions) +# - instead, the lower *mesh boundaries* are now identical with the underlying topography +# - the output routine has been vastly improved and is much more flexible now. + +# # Basic python imports and model settings + +# + +import underworld.visualisation as vis +from underworld import function as fn +import underworld as uw + +import matplotlib.pyplot as pyplot +import numpy as np +from scipy.spatial import distance + +import math +import os +import sys + +import time + +from scipy.signal import savgol_filter + +# details of the bottom curve +L = [160, 80, 40, 20, 10, 5] + +# make it command line compatible + +# make it command line compatible +if len(sys.argv): + try: + km_index = int(sys.argv[1]) + except: + km_index = 5 + +i = km_index + +systemDim = L[i] + +maxX = L[i] * 1000. +min_bed_height = 500. # we want a minimum of 500 m of rock beneath the ice +omega = 2.0 * np.pi / maxX +amplitude = 500. +average_bedthickness = 1000. +surface_height = average_bedthickness + amplitude + min_bed_height +maxY = surface_height +maxZ = maxX + +minY = minX = minZ = 0. + +g = 9.81 +ice_density = 910. + +A = 1e-16 +n = 3. + +resX = 32 +resY = 64 +resZ = 32 + +print("resX: " + str(resX) + " resY: " + str(resY) ) + +# generate output path +outputPath = os.path.join(os.path.abspath("."), "output_" + str(maxX) + "_res_" + str(resX) + "_x_" + str(resY) + "_x_" + str(resZ) + "/") + +if not os.path.exists(outputPath): + os.makedirs(outputPath) + +os.chdir(outputPath) + +delta_timestep = 1. # in years, used in the main loop +# after how many timesteps do we need new figures? + +cell_height = maxY / resY +cell_width = maxX / resX +cell_depth = maxZ / resZ +# - + +# # The mesh + +# + +elementType = "Q1/dQ0" + +mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType), + elementRes=(resX, resY, resZ), + minCoord=(minX, minY, minZ), + maxCoord=(maxX, maxY, maxZ), + periodic=[True, False, True]) + +submesh = mesh.subMesh + +# save the mesh +# mesh.save(outputPath + "mesh.h5") + +velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +#pressureField = uw.mesh.MeshVariable(mesh=mesh.subMesh, nodeDofCount=1) +pressureField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +viscosityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +strainRateField = mesh.add_variable(nodeDofCount=1) + +#pressureField.data[:] = 0. +velocityField.data[:] = [0., 0., 0.] +# - + +# # topo-function + +coord = fn.input() +z_bed_function = surface_height - average_bedthickness + amplitude * fn.math.sin(omega * coord[0]) * fn.math.sin(omega * coord[2]) + +# # Deform mesh - lower boundary + +# + +dx = (maxX - minX) / resX +dy = (maxX - maxY) / resY +dz = (maxZ - minZ) / resZ + +def mesh_deform_Ind(section, fixPoint_index, fixPoint, mi): + + section[fixPoint_index] = fixPoint + seqN = len(section) + + # fixPoint_index (int): specify the index of the section to be at the place need to be refined + # fixPoint: the position to be refined + # mi: representing the gradient of mesh resolution; the larger mi, the larger gradient + + for index in range(len(section)): + + maxCoord = np.max(section) + minCoord = np.min(section) + + if index < fixPoint_index: + + section[index] = minCoord + index * (fixPoint-minCoord) / fixPoint_index + zz_pow = (fixPoint - section[index])**mi + zz_pow_max = (fixPoint - minCoord)**mi + section[index] = fixPoint - (fixPoint-section[index]) * zz_pow / zz_pow_max + + if index > fixPoint_index: + + section[index] = fixPoint + (index-fixPoint_index)*(maxCoord-fixPoint) / (seqN-fixPoint_index-1) + zz_pow = (section[index] - fixPoint)**mi + zz_pow_max = (maxCoord - fixPoint)**mi + section[index] =fixPoint + (section[index]-fixPoint) * zz_pow / zz_pow_max + + return (section) + +with mesh.deform_mesh(): + + base = [] + + for indexx in range(resX + 1): + + for indexz in range(resZ + 1): + + start_x = dx * indexx + start_z = dz * indexz + + interface_y = z_bed_function.evaluate((start_x, 0., start_z))[0][0] + + ind = np.where( np.logical_and( abs(mesh.data[:, 0] - start_x) < 0.01*dx , + abs(mesh.data[:, 2] - start_z) < 0.01*dz ) ) + + mesh.data[ind[0],1] = mesh_deform_Ind(mesh.data[ind[0], 1], int(0), interface_y, 0.2) + + base.append( ind[0][ np.argmin( abs( mesh.data[ind, 1] - interface_y )[0] ) ] ) + +swarmCustom = uw.swarm.Swarm( mesh=mesh, particleEscape=True ) +result = swarmCustom.add_particles_with_coordinates(mesh.data[base]) +# - + +figMesh = vis.Figure(figsize=(1200,600)) +figMesh.append( vis.objects.Mesh(mesh)) +figMesh.window() + +# # A dummy swarm +# for evaluation + +# + +part_per_cell = 500 +swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# Initialise the 'materialVariable' data to represent different materials. +materialV = 0 # ice, isotropic +materialR = 1 # rock + +swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm, particlesPerCell=part_per_cell) +#swarmLayout = uw.swarm.layouts.PerCellGaussLayout( swarm=swarm, gaussPointCount=5 ) + +swarm.populate_using_layout(layout=swarmLayout) + +measurementSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# create pop control object +pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell) +pop_control2 = uw.swarm.PopulationControl(measurementSwarm) + +# ### Create a particle advection system +# +# Note that we need to set up one advector systems for each particle swarm (our global swarm and a separate one if we add passive tracers). +advector1 = uw.systems.SwarmAdvector(swarm=swarm, velocityField=velocityField, order=2) +advector2 = uw.systems.SwarmAdvector(swarm=measurementSwarm, velocityField=velocityField, order=2) +# - + +# # Boundary conditions + +# + +iWalls = mesh.specialSets["MinI_VertexSet"] + mesh.specialSets["MaxI_VertexSet"] +jWalls = mesh.specialSets["MinJ_VertexSet"] + mesh.specialSets["MaxJ_VertexSet"] +kWalls = mesh.specialSets["MinK_VertexSet"] + mesh.specialSets["MaxK_VertexSet"] + +# Surface points +topSet = mesh.specialSets["MaxJ_VertexSet"] + +leftSet = mesh.specialSets['Left_VertexSet'] +rightSet = mesh.specialSets['Right_VertexSet'] +botSet = mesh.specialSets["MinJ_VertexSet"] + +# Dirichlet +condition = uw.conditions.DirichletCondition(variable = velocityField, indexSetsPerDof=(botSet, botSet, botSet)) + +velocityField.data[:] = [0., 0., 0.] +# - + +strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient) +strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor) + +# # Viscosity, density, buoyancy + +# + +minViscosityIceFn = fn.misc.constant(1e+8 / 31556926) +maxViscosityIceFn = fn.misc.constant(1e+16 / 31556926) + +viscosityFnIceBase = 0.5 * A ** (-1./n) * (strainRate_2ndInvariantFn**((1.-n) / float(n))) +viscosityFn = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn) + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +densityFn = fn.misc.constant( ice_density ) + +surf_inclination = 0.5 * np.pi / 180. # 0.1 = Experiment C/D, 0.5 = Experiment A/B +z_hat = (math.sin(surf_inclination), - math.cos(surf_inclination), 0.) + +buoyancyFn = densityFn * z_hat * 9.81 +# - + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +# # Solver + +# + +stokes = uw.systems.Stokes( + velocityField=velocityField, + pressureField=pressureField, + voronoi_swarm=swarm, + conditions=condition, + fn_viscosity=viscosityFn, + fn_bodyforce=buoyancyFn, +) + +solver = uw.systems.Solver(stokes) + +#solver.set_inner_method("lu") +#solver.set_inner_method("superlu") +solver.set_inner_method("mumps") +#solver.set_inner_method("superludist") +#solver.set_inner_method("mg") +#solver.set_inner_method("nomg") + +# solver.set_penalty(1.0e21 / 31556926) # higher penalty = larger stability +# solver.options.scr.ksp_rtol = 1.0e-3 +#penalty = 1e3 +#solver.set_penalty(penalty) +#nl_tol = 2.e1 +nl_tol = 1.e-2 + +surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=topSet) +surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=topSet) + +def calibrate_pressure(): + + global pressureField + global surfaceArea + global surfacePressureIntegral + + (area,) = surfaceArea.evaluate() + (p0,) = surfacePressureIntegral.evaluate() + pressureField.data[:] -= p0 / area + + print (f'Calibration pressure {p0 / area}') + +# test it out +try: + exec_time = time.time() + #solver.solve(nonLinearIterate=True, nonLinearTolerance=nl_tol, callback_post_solve=calibrate_pressure) + + solver.solve(nonLinearIterate=True, callback_post_solve=calibrate_pressure) + exec_time = time.time() - exec_time + + # print full stats to a file + solver.print_stats() +except: + print("Solver died early..") + exit(0) + +print (f'Solving took: {exec_time} seconds') +# - + +#figStress = vis.Figure(figsize=(1200,600)) +#figStress.append( vis.objects.Mesh(mesh)) +#figStress.append(vis.objects.Points(swarm, shearStressFn, pointSize=4.0, colourBar=True, ))#fn_mask = materialVariable)) +#figStress.window() + +# # Output + +# + +#### Filename +outputFile = os.path.join(os.path.abspath("."), "jla"+"1a"+ str(systemDim).zfill(3) + ".csv") +print(outputFile) + +#### Smooth the stress +meshStressTensor = uw.mesh.MeshVariable(mesh, 6) +projectorStress = uw.utils.MeshVariable_Projection( meshStressTensor, devStressFn, type=0 ) +projectorStress.solve() + +#### Smooth the velocity +meshVelocity = uw.mesh.MeshVariable(mesh, 3) +projectorV = uw.utils.MeshVariable_Projection( meshVelocity, velocityField, type=0 ) +projectorV.solve() + +#### Smooth the pressure +meshP = uw.mesh.MeshVariable(mesh, 1) +projectorP = uw.utils.MeshVariable_Projection( meshP, pressureField, type=0 ) +projectorP.solve() + +#### Points +xpos = np.arange(start=0, stop=int(resX+1)) * maxX/resX +zpos = np.arange(start=0, stop=int(resZ+1)) * maxZ/resZ + +xz = np.array(np.meshgrid(xpos, zpos)).T.reshape(-1,2) + +sub = 1.*cell_height +add = 1.*cell_height + +surf_pos = np.insert(xz, 1, maxY - sub, axis=1 ) +base_pos = np.insert(xz, 1, 0., axis=1 ) + +topo_y = z_bed_function.evaluate(base_pos) + add +base_pos[:, 1] = topo_y[:,0] + +#### Get the surface velocity +#vxs = meshVelocity.evaluate(surf_pos).transpose()[0] +#vys = meshVelocity.evaluate(surf_pos).transpose()[1] +#vzs = meshVelocity.evaluate(surf_pos).transpose()[2] +vxs = velocityField.evaluate(surf_pos).transpose()[0] +vys = velocityField.evaluate(surf_pos).transpose()[1] +vzs = velocityField.evaluate(surf_pos).transpose()[2] + +vtots = np.sqrt( vxs*vxs + vys*vys + vzs*vzs ) + +#### Get the basal velocity +#vxb = meshVelocity.evaluate(base_pos).transpose()[0] +#vyb = meshVelocity.evaluate(base_pos).transpose()[1] +#vzb = meshVelocity.evaluate(base_pos).transpose()[2] +vxb = velocityField.evaluate(base_pos).transpose()[0] +vyb = velocityField.evaluate(base_pos).transpose()[1] +vzb = velocityField.evaluate(base_pos).transpose()[2] + +vtotb = np.sqrt( vxb*vxb + vyb*vyb + vzb*vzb ) + +#### Get the pressure +#P = meshP.evaluate(base_pos).squeeze() +P = pressureField.evaluate(base_pos).squeeze() + +#### Get the shearstress +sxz = meshStressTensor.evaluate(base_pos).squeeze()[:,3] +#sxz = devStressFn.evaluate(base_pos).squeeze()[:,3] + +sxy = meshStressTensor.evaluate(base_pos).squeeze()[:,4] +#sxz = devStressFn.evaluate(base_pos).squeeze()[:,3] + +#### only indices where z ~ 0.25 +ind = np.where(np.logical_and(xz[:,1] > 0.00 * maxZ , xz[:,1] < 1.00 * maxZ)) + +#### plot pressure from grid / theoretical / difference +print("DeltaP") +#pyplot.plot((maxY - base_ypos[:]) * 9.81 * 910, color='red') +smoothed_2dg = savgol_filter(P[ind], window_length = 7, polyorder = 2) +#pyplot.plot(P[ind], color='blue') +pyplot.plot(P[ind] - (maxY - base_pos[ind, 1].squeeze()) * 9.81 * 910., color='green') +pyplot.plot(smoothed_2dg, color='black') +pyplot.show() + +#### plot vx at surface +print("vs") +smoothed_2dg = savgol_filter(vxs[ind], window_length = 7, polyorder = 2) +#pyplot.plot(vxs[ind], color='red') +pyplot.plot(smoothed_2dg, color='black') +pyplot.show() + +### plot shear stress +print("Shear stress") +smoothed_2dg = savgol_filter(sxz[ind] / 1000, window_length = 7, polyorder = 2) +#pyplot.plot (sxz[ind] / 1000., color='red') +pyplot.plot (smoothed_2dg, color='black') +pyplot.show () + +#### output to file +with open(outputFile, "w") as text_file: + + for i in range(0, len(surf_pos[:, 0])): + + # Ausgabe [x] [y] + textline = str("{:.7f}".format(surf_pos[i, 0] / maxX)) + "\t" \ + + str("{:.7f}".format(surf_pos[i, 2] / maxZ)) + "\t" + + #Ausgabe Geschwindigkeiten Surface[vx] [vy] [vz] + textline += str("{:.7f}".format(vxs[i])) + "\t" + str("{:.7f}".format(vzs[i])) \ + + "\t" + str("{:.7f}".format(vys[i])) + "\t" + + #Ausgabe Geschwindigkeiten Basis [vx] [vy] + #textline += str("{:.7f}".format(vxb[i])) + "\t" + str("{:.7f}".format(vzb[i])) + "\t" + + # Scherspannung Basis Tensoren [Txz] [Tyz] + textline += str("{:.7f}".format(sxz[i] / 1000.)) + "\t" + str("{:.7f}".format(sxy[i] / 1000.)) + "\t" + + # Ausgabe delta p + textline += str("{:.7f}".format( (P[i] - float((maxY - base_pos[i, 1]) * 9.81 * 910 )) / 1000)) + "\n" + + + text_file.write(textline) +# - + + diff --git a/model_code_inputs/Exp_B-2D.py b/model_code_inputs/Exp_B-2D.py new file mode 100644 index 0000000..244da11 --- /dev/null +++ b/model_code_inputs/Exp_B-2D.py @@ -0,0 +1,770 @@ +#!/usr/bin/env python +# coding: utf-8 + +# # Basic python imports and model settings + +# In[41]: + + +import underworld.visualisation as vis + +from underworld import function as fn +import underworld as uw + +import matplotlib.pyplot as pyplot +import numpy as np +from scipy.spatial import distance + +import math +import os +import sys + +import time + +from scipy.signal import savgol_filter + +# deform the mesh geometry towards the ice-rock interface? +deform_mesh = False +perfect_mesh = True + +# details of the bottom curve +L = [160, 80, 40, 20, 10, 5] + +# make it command line compatible +if len(sys.argv): + try: + km_index = int(sys.argv[1]) + except: + km_index = 5 + +i = km_index + +maxX = L[i] * 1000. +min_bed_height = 500. # we want a minimum of 500 m of rock beneath the ice +omega = 2.0 * np.pi / maxX +amplitude = 500. +average_bedthickness = 1000. +surface_height = average_bedthickness + amplitude + min_bed_height +maxY = surface_height + +minY = minX = 0. + +g = 9.81 +ice_density = 910. + +A = 1e-16 +n = 3. + +resX = 250 +resY = 100 + +resX = 128 +resY = 64 + +#resX = 48 +#resY = 24 + +resX = 256 +resY = 128 + +print("resX: " + str(resX) + " resY: " + str(resY)) + +# generate output path +outputPath = os.path.join(os.path.abspath("."), "output_" + str(maxX) + "_res_" + str(resX) + "_x_" + str(resY) + "/") + +if not os.path.exists(outputPath): + os.makedirs(outputPath) + +os.chdir(outputPath) + +delta_timestep = 1. # in years, used in the main loop +# after how many timesteps do we need new figures? +update_figures_after_n_timesteps = 1 +number_of_deformation_lines = 11 + +number_of_deformation_points = 50000 +distance_between_deformation_lines = maxY / (number_of_deformation_lines + 1) + +cell_height = maxY / resY +cell_width = maxX / resX + + +# # Mesh + mesh variables + +# In[42]: + + +elementType = "Q1/dQ0" +#elementType = "Q2/dQ1" +#elementType = "Q1/dPc1" +#elementType = "Q2/dPc1" + +mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType), + elementRes=(resX, resY), + minCoord=(minX, minY), + maxCoord=(maxX, maxY), + periodic=[True, False]) + +submesh = mesh.subMesh + +# save the mesh +# mesh.save(outputPath + "mesh.h5") + +velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +#pressureField = uw.mesh.MeshVariable(mesh=mesh.subMesh, nodeDofCount=1) +pressureField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +viscosityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +strainRateField = mesh.add_variable(nodeDofCount=1) + +#pressureField.data[:] = 0. +velocityField.data[:] = [0., 0.] + +# Initialise the 'materialVariable' data to represent different materials. +materialA = 0 # accommodation layer, a.k.a. Sticky Air +materialV = 1 # ice, isotropic +materialR = 2 # rock +materialT = 5 # test material in order to test eg interface detection + +coord = fn.input() + +z_bed_function = surface_height - average_bedthickness + amplitude * fn.math.sin(omega * coord[0]) + + +# # Define the ice-rock / ice-air interface + +# In[43]: + + +botSet = mesh.specialSets['Bottom_VertexSet'] +topSet = mesh.specialSets['Top_VertexSet'] + +dx = (maxX - minX) / resX +iceRockInterface = [] +iceAirInterface = [] + +dx = (maxX - minX) / resX + +for index in range(resX+1): + + start_x = dx * index + + interface_y = surface_height - average_bedthickness + amplitude * np.sin(start_x * (np.pi * 2.) / (maxX-minX) ) + + #ind = np.where(abs(mesh.data[:,0] - start_x) < 0.01*dx) + iceRockInterface.append([start_x, interface_y]) + iceAirInterface.append([start_x, maxY]) + + +# # Deform mesh to be almost structurally conforming + +# In[15]: + + +def mesh_deform(section,fixPoint,mi): + + # fixPoint: the position to be refined + # mi: representing the gradient of mesh resolution; the larger mi, the larger gradient + # generally, mi ranges from 0.1 to 3, dependnig on the resolution + + # note from Till: + # I normalize it, because then it becomes more clear to me. + # normalization is not strictly necessary + normalize = maxY - minY + + section /= normalize + fixPoint /= normalize + + for index in range(len(section)): + + maxCoord = np.max(section) + minCoord = np.min(section) + + if section[index] < fixPoint: + zz_sqrt = (fixPoint - section[index])**mi + zz_sqrt_max = (fixPoint - minCoord)**mi + section[index] = fixPoint - (fixPoint - section[index]) * zz_sqrt / zz_sqrt_max + + if section[index] > fixPoint: + zz_sqrt = (section[index] - fixPoint)**mi + zz_sqrt_max = (maxCoord - fixPoint)**mi + section[index] = fixPoint + (section[index] - fixPoint) * zz_sqrt/zz_sqrt_max + + return (section * normalize) + +dx = (maxX - minX) / resX + +if deform_mesh: + + with mesh.deform_mesh(): + + for index in range(resX+1): + + start_x = dx * index + + interface_y = surface_height - average_bedthickness + amplitude * np.sin(start_x * (np.pi * 2.) / (maxX-minX) ) + + #print (start_x,interface_y) + #lx.append(start_x) + #ly.append(interface_y) + + #ind = np.where(abs(mesh.data[:,0] - start_x) < 0.01*dx) + ind = np.where(abs(mesh.data[:,0] - start_x) < 0.01*dx) + + mesh.data[ind[0],1] = mesh_deform(mesh.data[ind[0],1], interface_y, 0.25) + +# visualise the result +figMesh = vis.Figure(figsize=(1200,600)) +figMesh.append( vis.objects.Mesh(mesh) ) +figMesh.save_image("mesh_postdeform.png") +figMesh.show() + + +# # Deform mesh to a perfect body fit mesh + +# In[25]: + + +def mesh_deform_Ind(section,fixPoint_index,fixPoint,mi): + + section[int(fixPoint_index)] = fixPoint + seqN = len(section) + + # fixPoint_index (int): specify the index of the section to be at the place need to be refined + # fixPoint: the position to be refined + # mi: representing the gradient of mesh resolution; the larger mi, the larger gradient + for index in range(len(section)): + + maxCoord = np.max(section) + minCoord = np.min(section) + + if index < fixPoint_index: + section[index] = minCoord + index*(fixPoint-minCoord)/fixPoint_index + zz_sqrt = (fixPoint-section[index])**mi + zz_sqrt_max = (fixPoint-minCoord)**mi + section[index] = fixPoint-(fixPoint-section[index])*zz_sqrt/zz_sqrt_max + + if index > fixPoint_index: + section[index] = fixPoint + (index-fixPoint_index)*(maxCoord-fixPoint)/(seqN-fixPoint_index-1) + zz_sqrt = (section[index]-fixPoint)**mi + zz_sqrt_max = (maxCoord-fixPoint)**mi + section[index] =fixPoint+(section[index]-fixPoint)*zz_sqrt/zz_sqrt_max + + return (section) + +figMesh = vis.Figure(figsize=(1200,600)) +figMesh.append( vis.objects.Mesh(mesh) ) +figMesh.save_image("mesh_predeform.png") +figMesh.show() + +#picswarm = uw.swarm.VoronoiIntegrationSwarm(swarm) +#picswarm.repopulate() + +# visualise the result + +if (perfect_mesh): + + with mesh.deform_mesh(): + + for index in range(resX+1): + start_x = dx * index + + interface_y = surface_height - average_bedthickness + amplitude * np.sin(start_x * (np.pi * 2.) / (maxX-minX) ) + + ind = np.where(abs(mesh.data[:,0]-start_x)<0.01*dx) + + mesh.data[ind[0],1] = mesh_deform_Ind(mesh.data[ind[0],1],resY/2,interface_y,0.2) + # make the swarm belong the element that is the same as the in the regular mesh + + # visualise the result + figMesh = vis.Figure(figsize=(1200,600)) + figMesh.append( vis.objects.Mesh(mesh) ) + figMesh.save_image("mesh_deform_default_swarm.png") + figMesh.show() + + #with swarm.deform_swarm(): + #swarm.particleCoordinates.data[:] = uw.function.input().evaluate(picswarm) + + + + +# # Swarm + +# In[44]: + + +part_per_cell = 50 +swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +#swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm, particlesPerCell=part_per_cell) +swarmLayout = uw.swarm.layouts.PerCellGaussLayout( swarm=swarm, gaussPointCount=5 ) + +swarm.populate_using_layout(layout=swarmLayout) + +measurementSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# create pop control object +pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell) +pop_control2 = uw.swarm.PopulationControl(measurementSwarm) + +# ### Create a particle advection system +# +# Note that we need to set up one advector systems for each particle swarm (our global swarm and a separate one if we add passive tracers). +advector1 = uw.systems.SwarmAdvector(swarm=swarm,velocityField=velocityField, order=2) +advector2 = uw.systems.SwarmAdvector(swarm=measurementSwarm, velocityField=velocityField, order=2) + +# Tracking different materials + +materialVariable = swarm.add_variable(dataType="int", count=1) + +numbMeasurementPoints = resX + 1 +xloc = np.linspace(0, maxX, numbMeasurementPoints).reshape(-1,1) +yloc = (surface_height - average_bedthickness + amplitude * np.sin(omega * xloc)).reshape(-1,1) +xycoor = np.concatenate((xloc,yloc),axis = 1) + +measurementSwarm.add_particles_with_coordinates(xycoor) + +particleDensity = swarm.add_variable(dataType="double", count=1) +particleDensity.data[:] = 0.0 + +coord = fn.input() + +conditions = [(coord[1] > surface_height, materialA), + (coord[1] < z_bed_function, materialR), + (True, materialV)] + +materialVariable.data[:] = fn.branching.conditional(conditions).evaluate(swarm) + +#pyplot.plot(measurementSwarm.data[:,0], measurementSwarm.data[:,1], color='black') + +figMesh = vis.Figure(figsize=(1200,600)) +figMesh.append( vis.objects.Mesh(mesh) ) +figMesh.append( vis.objects.Points( swarm, materialVariable, pointSize=10.0 ) ) +figMesh.save_image("mesh_deform.png") +figMesh.show() + + +# In[45]: + + +# find and index elements that contain mixed materials of materialA and materialB +ind1 = np.where(materialVariable.data[:]==materialV) +ind0 = np.where(materialVariable.data[:]==materialR) +index_common = np.intersect1d(swarm.owningCell.data[ind1[0]],swarm.owningCell.data[ind0[0]]) +print (index_common) + + +# # Functions + +# In[46]: + + +strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient) +strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor) + +minViscosityIceFn = fn.misc.constant(1e+10 / 3.1536e7) +maxViscosityIceFn = fn.misc.constant(1e+15 / 3.1536e7) + +viscosityFnAir = fn.misc.constant(1e6 / 3.1536e7) +viscosityFnRock = fn.misc.constant(1e22 / 3.1536e7) + +viscosityFnIceBase = 0.5 * A ** (-1./n) * (strainRate_2ndInvariantFn**((1.-n) / float(n))) +viscosityFnIce = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn) + +viscosityMap = { + materialV: viscosityFnIce, + materialA: viscosityFnAir, + materialR: viscosityFnRock, + } + +viscosityFn = fn.branching.map( fn_key=materialVariable, mapping=viscosityMap ) + +logViscosityFn = fn.math.log10( fn.misc.max( fn.misc.min( viscosityFnIceBase, viscosityFnRock ), viscosityFnAir ) ) + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +densityFnAir = fn.misc.constant( 0. ) +densityFnIce = fn.misc.constant( ice_density ) +densityFnRock = fn.misc.constant( 2700. ) + +densityMap = { + materialA: densityFnAir, + materialV: densityFnIce, + materialR: densityFnRock + } + +densityFn = fn.branching.map(fn_key=materialVariable, mapping=densityMap) + +particleDensity.data[:] = densityFn.evaluate(swarm) + +surf_inclination = 0.5 * np.pi / 180. # 0.1 = Experiment D, 0.5 = Experiment B +#surf_inclination = 0. +z_hat = (math.sin(surf_inclination), - math.cos(surf_inclination)) +#z_hat = (0.00872653549, -0.99996192306417128874) + +buoyancyFn = densityFn * z_hat * 9.81 + + +# # Solver and boundary conditions + +# In[47]: + + +iWalls = mesh.specialSets["MinI_VertexSet"] + mesh.specialSets["MaxI_VertexSet"] +jWalls = mesh.specialSets["MinJ_VertexSet"] + mesh.specialSets["MaxJ_VertexSet"] +base = mesh.specialSets["MinJ_VertexSet"] +top = mesh.specialSets["MaxJ_VertexSet"] + +velocityField.data[:] = [0., 0.] + +leftSet = mesh.specialSets['Left_VertexSet'] +rightSet = mesh.specialSets['Right_VertexSet'] + +### Dirichlet +condition1 = uw.conditions.DirichletCondition(variable=velocityField,indexSetsPerDof=(botSet, botSet)) + +velocityField.data[:] = [0., 0.] + +stokes = uw.systems.Stokes( + velocityField=velocityField, + pressureField=pressureField, + voronoi_swarm=swarm, + conditions=[ + condition1, + ], + fn_viscosity=viscosityFn, + fn_bodyforce=buoyancyFn, +) + +solver = uw.systems.Solver(stokes) + +#solver.set_inner_method("lu") +#solver.set_inner_method("superlu") +solver.set_inner_method("mumps") +# solver.set_inner_method("superludist") +# solver.set_inner_method("mg") +#solver.set_inner_method("nomg") + +# solver.set_penalty(1.0e10) # higher penalty = larger stability +# solver.options.scr.ksp_rtol = 1.0e-3 + +# nl_tol = 2.e1 +nl_tol = 5.e-3 + +surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=top) +surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=top) + +def calibrate_pressure(): + + global pressureField + global surfaceArea + global surfacePressureIntegral + + (area,) = surfaceArea.evaluate() + (p0,) = surfacePressureIntegral.evaluate() + pressureField.data[:] -= p0 / area + + print (f'Calibration pressure {p0 / area}') + +# test it out +try: + exec_time = time.time() + # solver.solve(nonLinearIterate=True, nonLinearTolerance=nl_tol, callback_post_solve=calibrate_pressure) + solver.solve(nonLinearIterate=True, callback_post_solve=calibrate_pressure) + # solver.solve(nonLinearIterate=True) + exec_time = time.time() - exec_time + + # print time to a file + with open('../time.txt', 'a') as f: + f.write('length,' + str(maxX) + ',x_res:,' + str(resX) + ',y_res:,' + str(resY) + ',time in secs:,' + str(exec_time) + '\n') + + # print full stats to a file + original_stdout = sys.stdout # Save a reference to the original standard output + + with open('../stats_' + "output_" + str(maxX) + "_res_" + str(resX) + '_x_' + str(resY) + '.txt', 'w') as f: + sys.stdout = f # Change the standard output to the file we created. + solver.print_stats() + sys.stdout = original_stdout # Reset the standard output to its original value + + solver.print_stats() +except: + print("Solver died early..") + exit(0) + + +# # Output + +# In[48]: + + +meshStressTensor = uw.mesh.MeshVariable(mesh, 3 ) +projectorStress = uw.utils.MeshVariable_Projection( meshStressTensor, devStressFn, type=0 ) +projectorStress.solve() + +## correct the pressure +meshCorrectedPressure = uw.mesh.MeshVariable(mesh, 1 ) +meshSecondCorrectedPressure = mesh.add_variable( 1 ) + +## a) from the pressureField +meshCorrectedPress = uw.utils.MeshVariable_Projection( meshCorrectedPressure, pressureField, type=0 ) +meshCorrectedPress.solve() + +## b) from the stranirate tensor +pressureFn = (strainRateTensor[0] + strainRateTensor[1]) * viscosityFn +meshSecondCorrectedPress = uw.utils.MeshVariable_Projection( meshSecondCorrectedPressure, pressureFn, type=1 ) +meshSecondCorrectedPress.solve() + +## shear stress as saved to disk +shearStressFn = 2.0 * viscosityFn * strainRateTensor[2] +meshShearStress = mesh.add_variable( 1 ) + +projectorStress = uw.utils.MeshVariable_Projection( meshShearStress, shearStressFn, type=0 ) +projectorStress.solve() + +## second invariant of stress as saved to disk +secInvStressFn = 2.0 * viscosityFn * strainRate_2ndInvariantFn +secInvStress = mesh.add_variable( 1 ) + +projectorStress = uw.utils.MeshVariable_Projection( secInvStress, secInvStressFn, type=0 ) +projectorStress.solve() + +# save to disc +outputFile = os.path.join(os.path.abspath("."), outputPath + "output_" + str(maxX) + ".csv") + +#### + +x = np.linspace(0, maxX, resX+1) +interfacex = [item[0] for item in iceRockInterface] +interfacey = [item[1] for item in iceRockInterface] + +airinterfacey = [maxY for item in range(resX + 1)] + +iceRockInterface = np.array(iceRockInterface) +iceAirInterface = np.array(iceAirInterface) + +add = 1. * cell_height +sub = - 1. * cell_height + +#add = 5. +#sub = - 5. + +### + +shearstress_xy_above = [] +corr_shearstress_xy_above = [] +shearstress_xy_below = [] +corr_shearstress_xy_below = [] + +for i,j in zip(interfacex,interfacey): + + shearstress_xy_above.append(shearStressFn.evaluate((i,j + add))[0][0]) + corr_shearstress_xy_above.append(meshStressTensor.evaluate((i,j + add))[0][2]) + + shearstress_xy_below.append(shearStressFn.evaluate((i,j + sub))[0][0]) + corr_shearstress_xy_below.append(meshStressTensor.evaluate((i,j + sub))[0][2]) + +secinvstress_above = [] +corr_secinvstress_above = [] +secinvstress_below = [] +corr_secinvstress_below = [] + +for i,j in zip(interfacex,interfacey): + + secinvstress_above.append(secInvStressFn.evaluate((i,j + add))[0][0]) + corr_secinvstress_above.append(secInvStress.evaluate((i,j + add))[0][0]) + + secinvstress_below.append(secInvStressFn.evaluate((i,j + sub))[0][0]) + corr_secinvstress_below.append(secInvStress.evaluate((i,j + sub))[0][0]) + +#### + +pressure = [] +corr_pressure = [] +for i,j in zip(interfacex,interfacey): + pressure.append(pressureField.evaluate((i, j + add))[0][0]) + corr_pressure.append(meshCorrectedPressure.evaluate((i, j + add))[0][0]) + +with open(outputFile, "w") as text_file: + + text_file.write("X," + "Y," + "surf vx," + "surf vy," + "tauxy integr. above," + "tauxy dir. above," + "secinvare integr. above," + "secinvar dir. above," + "tauxy integr. below," + "tauxy dir. below," + "secinvare integr. below," + "secinvar dir. below," + "P integr.," + "P dir.," + "\n") + + for i in range(0,len(interfacex)): + + textline = str(interfacex[i]) + "," + str(interfacey[i]) + "," + str(velocityField.evaluate((interfacex[i], airinterfacey[i]))[0][0]) + "," + str(velocityField.evaluate((interfacex[i], airinterfacey[i]))[0][1]) + "," + str(corr_shearstress_xy_above[i]) + "," + str(shearstress_xy_above[i]) + "," + str(corr_secinvstress_above[i]) + "," + str(secinvstress_above[i]) + "," + str(corr_shearstress_xy_below[i]) + "," + str(shearstress_xy_below[i]) + "," + str(corr_secinvstress_below[i]) + "," + str(secinvstress_below[i]) + "," + str(corr_pressure[i]) + "," + str(pressure[i]) + "\n" + + text_file.write(textline) + +# In[116]: + +# plot saved files + +outputFile = outputPath + "output_" + str(maxX) + ".csv" +a = np.loadtxt(open(outputFile, "rb"), delimiter=",", skiprows=1) +a = a.T + +print ("topo") +pyplot.scatter (a[0], a[1]) +yhat = savgol_filter(a[1], 13, 7) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("topo.png") + +print ("top x vel") +pyplot.scatter (a[0], a[2]) +yhat = savgol_filter(a[2], 13, 7) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("top x vel.png") + +print ("top y vel") +pyplot.scatter (a[0], a[3]) +yhat = savgol_filter(a[3], 13, 9) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("top y vel.png") + +print ("top total vel") +pyplot.scatter (a[0], np.sqrt(a[3]**2 + a[2]**2)) +yhat = savgol_filter(np.sqrt(a[3]**2 + a[2]**2), 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("top total vel.png") + +print ("tau integr. above") +pyplot.scatter (a[0], a[4]) +yhat = savgol_filter(a[4], 13, 4) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("tau integr. above.png") + +print ("tau integr. below") +pyplot.scatter (a[0], a[8]) +yhat = savgol_filter(a[8], 13, 4) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("tau integr. below.png") + +print ("tau dir. above") +pyplot.scatter (a[0], a[5]) +yhat = savgol_filter(a[5], 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("tau dir. above.png") + +print ("tau dir. below") +pyplot.scatter (a[0], a[9]) +yhat = savgol_filter(a[9], 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("tau dir. below.png") + +print ("sec inv integr. above") +pyplot.scatter (a[0], a[6]) +yhat = savgol_filter(a[6], 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("sec inv integr. above.png") + +print ("sec inv integr. below") +pyplot.scatter (a[0], a[10]) +yhat = savgol_filter(a[10], 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("sec inv integr. below.png") + +print ("sec inv dir. above") +pyplot.scatter (a[0], a[7]) +yhat = savgol_filter(a[7], 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("sec inv dir. above.png") + +print ("sec inv dir. below") +pyplot.scatter (a[0], a[11]) +yhat = savgol_filter(a[11], 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("sec inv dir. below.png") + +print ("basal pressure integr.") +pyplot.scatter (a[0], a[12]) +yhat = savgol_filter(a[12], 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("basal pressure integr.png") + +print ("basal pressure dir.") +pyplot.scatter (a[0], a[13]) +yhat = savgol_filter(a[13], 13, 5) +pyplot.plot(a[0], yhat, color='red') +pyplot.show() +pyplot.savefig("basal pressure dir.png") + + +# In[ ]: + + +# plot figures + +figinflow = vis.Figure(figsize=(1800,500), title="free slip with in/out flow") +figinflow.append(vis.objects.VectorArrows(mesh, velocityField)) +figinflow.append(vis.objects.Surface(mesh, uw.function.math.dot(velocityField,velocityField), colours="gebco")) +figinflow.save_image(outputPath + "velocity_" + str(maxX) + ".png") +figinflow.show() + +figMaterial = vis.Figure(figsize=(1800, 500), title="Material") +figMaterial.append(vis.objects.Points( swarm, materialVariable, pointSize=1.0)) +figMaterial.append( vis.objects.Mesh(mesh) ) +figMaterial.save_image(outputPath + "material_" + str(maxX) + ".png") +figMaterial.show() + +figDensity = vis.Figure(figsize=(1800, 500), title="Density") +figDensity.append(vis.objects.Points( swarm, particleDensity, pointSize=1.0)) +figDensity.save_image(outputPath + "density_" + str(maxX) + ".png") +figDensity.show() + +figViscosity = vis.Figure(figsize=(1800, 500), title="viscosity") +figViscosity.append(vis.objects.Surface(mesh, logViscosityFn)) +figViscosity.save_image(outputPath + "logviscosity_" + str(maxX) + ".png") +figViscosity.show() + +figPressure = vis.Figure(figsize=(1800, 500), title="pressure") +figPressure.append(vis.objects.Surface(mesh, pressureField)) +figPressure.save_image(outputPath + "pressure_" + str(maxX) + ".png") +figPressure.show() + +figShearStress = vis.Figure(figsize=(1800, 500), title="corr_shearstress_xy") +figShearStress.append(vis.objects.Surface(mesh, meshShearStress)) +figShearStress.save_image(outputPath + "corr_shearstress_xy" + str(maxX) + ".png") +figShearStress.show() + + +# In[ ]: + + +# finally save meshvars, swarmvars, xdmf vars +xdmf_info_mesh = mesh.save('mesh.h5') +xdmf_info_meshVelocityField = velocityField.save('meshVelocityField.h5') +xdmf_info_meshShearStress = meshShearStress.save('meshShearStress.h5') +xdmf_info_meshCorrectedPressure = meshCorrectedPressure.save('meshCorrectedPressure.h5') + +# swarm +xdmf_info_swarm = swarm.save('swarm.h5') +xdmf_info_swarmMaterialVariable = materialVariable.save('swarmMaterialVariable.h5') + +# xdmf mesh +velocityField.xdmf('meshVelocityField.xdmf', xdmf_info_meshVelocityField, "velocityField", xdmf_info_mesh, "TheMesh", modeltime=0.0) +meshShearStress.xdmf('meshShearStress.xdmf', xdmf_info_meshShearStress, "meshShearStress", xdmf_info_mesh, "TheMesh", modeltime=0.0) +meshCorrectedPressure.xdmf('meshCorrectedPressure.xdmf', xdmf_info_meshCorrectedPressure, "correctedPressureField", xdmf_info_mesh, "TheMesh", modeltime=0.0) + +# xdmf swarm +materialVariable.xdmf('swarmMaterialVariable.xdmf', xdmf_info_swarmMaterialVariable, "material", xdmf_info_swarm, "TheSwarm", modeltime=0.0) + + +# In[ ]: + + + + diff --git a/model_code_inputs/Exp_B-3D.py b/model_code_inputs/Exp_B-3D.py new file mode 100644 index 0000000..26cf324 --- /dev/null +++ b/model_code_inputs/Exp_B-3D.py @@ -0,0 +1,450 @@ +# --- +# jupyter: +# jupytext: +# formats: ipynb,md,py:light +# text_representation: +# extension: .py +# format_name: light +# format_version: '1.5' +# jupytext_version: 1.13.5 +# kernelspec: +# display_name: Python 3 (ipykernel) +# language: python +# name: python3 +# --- + +# This model is from Jan 2022. It contains important improvements over previous models, namely: +# +# - it doesn't need particles any more +# - (but still uses them in order to evaluate and visualize certain functions) +# - instead, the lower *mesh boundaries* are now identical with the underlying topography +# - the output routine has been vastly improved and is much more flexible now. + +# # Basic python imports and model settings + +# + +import underworld.visualisation as vis +from underworld import function as fn +import underworld as uw + +import matplotlib.pyplot as pyplot +import numpy as np +from scipy.spatial import distance + +import math +import os +import sys + +import time + +from scipy.signal import savgol_filter + +# details of the bottom curve +L = [160, 80, 40, 20, 10, 5] + +# make it command line compatible + +# make it command line compatible +if len(sys.argv): + try: + km_index = int(sys.argv[1]) + except: + km_index = 0 + +i = km_index + +systemDim = L[i] + +maxX = L[i] * 1000. +min_bed_height = 500. # we want a minimum of 500 m of rock beneath the ice +omega = 2.0 * np.pi / maxX +amplitude = 500. +average_bedthickness = 1000. +surface_height = average_bedthickness + amplitude + min_bed_height +maxY = surface_height +maxZ = maxX + +minY = minX = minZ = 0. + +g = 9.81 +ice_density = 910. + +A = 1e-16 +n = 3. + +resX = 32 +resY = 64 +resZ = 32 + +print("resX: " + str(resX) + " resY: " + str(resY) ) + +# generate output path +outputPath = os.path.join(os.path.abspath("."), "output_" + str(maxX) + "_res_" + str(resX) + "_x_" + str(resY) + "_x_" + str(resZ) + "/") + +if not os.path.exists(outputPath): + os.makedirs(outputPath) + +os.chdir(outputPath) + +delta_timestep = 1. # in years, used in the main loop +# after how many timesteps do we need new figures? + +cell_height = maxY / resY +cell_width = maxX / resX +cell_depth = maxZ / resZ +# - + +# # The mesh + +# + +elementType = "Q1/dQ0" + +mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType), + elementRes=(resX, resY, resZ), + minCoord=(minX, minY, minZ), + maxCoord=(maxX, maxY, maxZ), + periodic=[True, False, True]) + +submesh = mesh.subMesh + +# save the mesh +# mesh.save(outputPath + "mesh.h5") + +velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +#pressureField = uw.mesh.MeshVariable(mesh=mesh.subMesh, nodeDofCount=1) +pressureField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +viscosityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +strainRateField = mesh.add_variable(nodeDofCount=1) + +#pressureField.data[:] = 0. +velocityField.data[:] = [0., 0., 0.] +# - + +# # topo-function + +coord = fn.input() +z_bed_function = surface_height - average_bedthickness + amplitude * fn.math.sin(omega * coord[0]) # * fn.math.sin(omega * coord[2]) + +# # Deform mesh - lower boundary + +# + +dx = (maxX - minX) / resX +dy = (maxX - maxY) / resY +dz = (maxZ - minZ) / resZ + +def mesh_deform_Ind(section, fixPoint_index, fixPoint, mi): + + section[fixPoint_index] = fixPoint + seqN = len(section) + + # fixPoint_index (int): specify the index of the section to be at the place need to be refined + # fixPoint: the position to be refined + # mi: representing the gradient of mesh resolution; the larger mi, the larger gradient + + for index in range(len(section)): + + maxCoord = np.max(section) + minCoord = np.min(section) + + if index < fixPoint_index: + + section[index] = minCoord + index * (fixPoint-minCoord) / fixPoint_index + zz_pow = (fixPoint - section[index])**mi + zz_pow_max = (fixPoint - minCoord)**mi + section[index] = fixPoint - (fixPoint-section[index]) * zz_pow / zz_pow_max + + if index > fixPoint_index: + + section[index] = fixPoint + (index-fixPoint_index)*(maxCoord-fixPoint) / (seqN-fixPoint_index-1) + zz_pow = (section[index] - fixPoint)**mi + zz_pow_max = (maxCoord - fixPoint)**mi + section[index] =fixPoint + (section[index]-fixPoint) * zz_pow / zz_pow_max + + return (section) + +with mesh.deform_mesh(): + + base = [] + + for indexx in range(resX + 1): + + for indexz in range(resZ + 1): + + start_x = dx * indexx + start_z = dz * indexz + + interface_y = z_bed_function.evaluate((start_x, 0., start_z))[0][0] + + ind = np.where( np.logical_and( abs(mesh.data[:, 0] - start_x) < 0.01*dx , + abs(mesh.data[:, 2] - start_z) < 0.01*dz ) ) + + mesh.data[ind[0],1] = mesh_deform_Ind(mesh.data[ind[0], 1], int(0), interface_y, 0.2) + + base.append( ind[0][ np.argmin( abs( mesh.data[ind, 1] - interface_y )[0] ) ] ) + +swarmCustom = uw.swarm.Swarm( mesh=mesh, particleEscape=True ) +result = swarmCustom.add_particles_with_coordinates(mesh.data[base]) +# - + +figMesh = vis.Figure(figsize=(1200,600)) +figMesh.append( vis.objects.Mesh(mesh)) +figMesh.window() + +# # A dummy swarm +# for evaluation + +# + +part_per_cell = 500 +swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# Initialise the 'materialVariable' data to represent different materials. +materialV = 0 # ice, isotropic +materialR = 1 # rock + +swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm, particlesPerCell=part_per_cell) +#swarmLayout = uw.swarm.layouts.PerCellGaussLayout( swarm=swarm, gaussPointCount=5 ) + +swarm.populate_using_layout(layout=swarmLayout) + +measurementSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# create pop control object +pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell) +pop_control2 = uw.swarm.PopulationControl(measurementSwarm) + +# ### Create a particle advection system +# +# Note that we need to set up one advector systems for each particle swarm (our global swarm and a separate one if we add passive tracers). +advector1 = uw.systems.SwarmAdvector(swarm=swarm, velocityField=velocityField, order=2) +advector2 = uw.systems.SwarmAdvector(swarm=measurementSwarm, velocityField=velocityField, order=2) +# - + +# # Boundary conditions + +# + +iWalls = mesh.specialSets["MinI_VertexSet"] + mesh.specialSets["MaxI_VertexSet"] +jWalls = mesh.specialSets["MinJ_VertexSet"] + mesh.specialSets["MaxJ_VertexSet"] +kWalls = mesh.specialSets["MinK_VertexSet"] + mesh.specialSets["MaxK_VertexSet"] + +# Surface points +topSet = mesh.specialSets["MaxJ_VertexSet"] + +leftSet = mesh.specialSets['Left_VertexSet'] +rightSet = mesh.specialSets['Right_VertexSet'] +botSet = mesh.specialSets["MinJ_VertexSet"] + +# Dirichlet +condition = uw.conditions.DirichletCondition(variable = velocityField, indexSetsPerDof=(botSet, botSet, botSet)) + +velocityField.data[:] = [0., 0., 0.] +# - + +strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient) +strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor) + +# # Viscosity, density, buoyancy + +# + +minViscosityIceFn = fn.misc.constant(1e+8 / 31556926) +maxViscosityIceFn = fn.misc.constant(1e+16 / 31556926) + +viscosityFnIceBase = 0.5 * A ** (-1./n) * (strainRate_2ndInvariantFn**((1.-n) / float(n))) +viscosityFn = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn) + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +densityFn = fn.misc.constant( ice_density ) + +surf_inclination = 0.5 * np.pi / 180. # 0.1 = Experiment C/D, 0.5 = Experiment A/B +z_hat = (math.sin(surf_inclination), - math.cos(surf_inclination), 0.) + +buoyancyFn = densityFn * z_hat * 9.81 +# - + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +# # Solver + +# + +stokes = uw.systems.Stokes( + velocityField=velocityField, + pressureField=pressureField, + voronoi_swarm=swarm, + conditions=condition, + fn_viscosity=viscosityFn, + fn_bodyforce=buoyancyFn, +) + +solver = uw.systems.Solver(stokes) + +#solver.set_inner_method("lu") +#solver.set_inner_method("superlu") +solver.set_inner_method("mumps") +#solver.set_inner_method("superludist") +#solver.set_inner_method("mg") +#solver.set_inner_method("nomg") + +# solver.set_penalty(1.0e21 / 31556926) # higher penalty = larger stability +# solver.options.scr.ksp_rtol = 1.0e-3 +#penalty = 1e3 +#solver.set_penalty(penalty) +#nl_tol = 2.e1 +nl_tol = 1.e-2 + +surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=topSet) +surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=topSet) + +def calibrate_pressure(): + + global pressureField + global surfaceArea + global surfacePressureIntegral + + (area,) = surfaceArea.evaluate() + (p0,) = surfacePressureIntegral.evaluate() + pressureField.data[:] -= p0 / area + + print (f'Calibration pressure {p0 / area}') + +# test it out +try: + exec_time = time.time() + #solver.solve(nonLinearIterate=True, nonLinearTolerance=nl_tol, callback_post_solve=calibrate_pressure) + + solver.solve(nonLinearIterate=True, callback_post_solve=calibrate_pressure) + exec_time = time.time() - exec_time + + # print full stats to a file + solver.print_stats() +except: + print("Solver died early..") + exit(0) + +print (f'Solving took: {exec_time} seconds') +# - + +#figStress = vis.Figure(figsize=(1200,600)) +#figStress.append( vis.objects.Mesh(mesh)) +#figStress.append(vis.objects.Points(swarm, shearStressFn, pointSize=4.0, colourBar=True, ))#fn_mask = materialVariable)) +#figStress.window() + +# # Output + +# + +#### Filename +outputFile = os.path.join(os.path.abspath("."), "jla"+"1b"+ str(systemDim).zfill(3) + ".csv") +print(outputFile) + +#### Smooth the stress +meshStressTensor = uw.mesh.MeshVariable(mesh, 6) +projectorStress = uw.utils.MeshVariable_Projection( meshStressTensor, devStressFn, type=0 ) +projectorStress.solve() + +#### Smooth the velocity +meshVelocity = uw.mesh.MeshVariable(mesh, 3) +projectorV = uw.utils.MeshVariable_Projection( meshVelocity, velocityField, type=0 ) +projectorV.solve() + +#### Smooth the pressure +meshP = uw.mesh.MeshVariable(mesh, 1) +projectorP = uw.utils.MeshVariable_Projection( meshP, pressureField, type=0 ) +projectorP.solve() + +#### Points +xpos = np.arange(start=0, stop=int(resX+1)) * maxX / resX +zpos = np.arange(start=0, stop=int(resZ+1)) * maxZ / resZ + +xz = np.array(np.meshgrid(xpos, zpos)).T.reshape(-1,2) + +sub = 1. * cell_height +add = 1. * cell_height + +surf_pos = np.insert(xz, 1, maxY - sub, axis=1 ) +base_pos = np.insert(xz, 1, 0., axis=1 ) + +surf_y = z_bed_function.evaluate(xz) +base_pos[:, 1] = surf_y[:,0] + add + +#### Get the surface velocity +vxs = meshVelocity.evaluate(surf_pos).transpose()[0] +vys = meshVelocity.evaluate(surf_pos).transpose()[1] +vzs = meshVelocity.evaluate(surf_pos).transpose()[2] + +vtots = np.sqrt( vxs*vxs + vys*vys + vzs*vzs ) + +#### Get the basal velocity +vxb = meshVelocity.evaluate(base_pos).transpose()[0] +vyb = meshVelocity.evaluate(base_pos).transpose()[1] +vzb = meshVelocity.evaluate(base_pos).transpose()[2] + +vtotb = np.sqrt( vxb*vxb + vyb*vyb + vzb*vzb ) + +#### Get the pressure +P = meshP.evaluate(base_pos).squeeze() +#P = pressureField.evaluate(base_pos).squeeze() + +#### Get the shearstress +sxz = meshStressTensor.evaluate(base_pos).squeeze()[:,3] +#sxz = devStressFn.evaluate(base_pos).squeeze()[:,3] + +sxy = meshStressTensor.evaluate(base_pos).squeeze()[:,4] +#sxz = devStressFn.evaluate(base_pos).squeeze()[:,3] + +#### only indices where z ~ 0.25 +ind = np.where(np.logical_and(xz[:,1] > 0.22 * maxZ , xz[:,1] < 0.28 * maxZ)) + +#### plot pressure from grid / theoretical / difference +print("DeltaP") +#pyplot.plot((maxY - base_ypos[:]) * 9.81 * 910, color='red') +smoothed_2dg = savgol_filter(P[ind], window_length = 7, polyorder = 2) +#pyplot.plot(P[ind], color='blue') + +pyplot.plot((P[ind] - (maxY - base_pos[ind, 1].squeeze()) * 9.81 * 910.) / 1000. , color='green') +pyplot.plot((P[ind]) / 1000. , color='green') +pyplot.plot(((maxY - base_pos[ind, 1].squeeze()) * 9.81 * 910.) / 1000. , color='red') +pyplot.show() + +#### plot vx at surface +print("vs") +smoothed_2dg = savgol_filter(vxs[ind], window_length = 7, polyorder = 2) +#pyplot.plot(vxs[ind], color='red') +pyplot.plot(smoothed_2dg, color='black') +pyplot.show() + +### plot shear stress +print("Shear stress") +smoothed_2dg = savgol_filter(sxz[ind] / 1000, window_length = 7, polyorder = 2) +pyplot.plot(smoothed_2dg) +pyplot.show() + +#### output to file +with open(outputFile, "w") as text_file: + + for i in ind[0]: + + # Ausgabe [x] [y] + textline = str("{:.7f}".format(surf_pos[i, 0] / maxX)) + "\t" \ + #+ str("{:.7f}".format(surf_pos[i, 2] / maxZ)) + "\t" + + #Ausgabe Geschwindigkeiten Surface[vx] [vy] [vz] + textline += str("{:.7f}".format(vxs[i])) + "\t"# + str("{:.7f}".format(vzs[i])) \ + textline += str("{:.7f}".format(vys[i])) + "\t" + + #Ausgabe Geschwindigkeiten Basis [vx] [vy] + textline += str("{:.7f}".format(vxb[i])) + "\t"# + str("{:.7f}".format(vzb[i])) + "\t" + + # Scherspannung Basis Tensoren [Txz] [Tyz] + textline += str("{:.7f}".format(sxz[i] / 1000.)) + "\t"# + str("{:.7f}".format(sxy[i] / 1000.)) + "\t" + + # Ausgabe delta p + textline += str("{:.7f}".format( (P[i] - float((surf_pos[i, 1]- base_pos[i, 1]) * 9.81 * 910 )) / 1000)) + "\n" + + text_file.write(textline) + #print(textline) +# - + + diff --git a/model_code_inputs/Exp_B_2D.ipynb b/model_code_inputs/Exp_B_2D.ipynb new file mode 100644 index 0000000..9d38da5 --- /dev/null +++ b/model_code_inputs/Exp_B_2D.ipynb @@ -0,0 +1,931 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "ae424bc3", + "metadata": {}, + "outputs": [], + "source": [ + "import underworld.visualisation as vis\n", + "\n", + "from underworld import function as fn\n", + "import underworld as uw\n", + "\n", + "import matplotlib.pyplot as pyplot\n", + "import numpy as np\n", + "from scipy.spatial import distance\n", + "\n", + "import math\n", + "import os\n", + "import sys\n", + "\n", + "import time\n", + "\n", + "from scipy.signal import savgol_filter\n", + "\n", + "# deform the mesh geometry towards the ice-rock interface?\n", + "deform_mesh = False\n", + "perfect_mesh = True" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "ff80bfe6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "resX: 64 resY: 32\n" + ] + } + ], + "source": [ + "# details of the bottom curve\n", + "# L = [160, 80, 40, 20, 10, 5]\n", + "L = 10\n", + "# make it command line compatible\n", + "if len(sys.argv):\n", + " try:\n", + " km_index = int(sys.argv[1])\n", + " except:\n", + " km_index = 5\n", + "\n", + "maxX = L * 1000.\n", + "min_bed_height = 500. # we want a minimum of 500 m of rock beneath the ice\n", + "omega = 2.0 * np.pi / maxX\n", + "amplitude = 500.\n", + "average_bedthickness = 1000.\n", + "surface_height = average_bedthickness + amplitude + min_bed_height\n", + "maxY = surface_height\n", + "\n", + "minY = minX = 0.\n", + "\n", + "g = 9.81\n", + "ice_density = 910.\n", + "\n", + "A = 1e-16\n", + "n = 3.\n", + "\n", + "\n", + "resX = 64\n", + "resY = 32\n", + "\n", + "\n", + "print(\"resX: \" + str(resX) + \" resY: \" + str(resY))" + ] + }, + { + "cell_type": "markdown", + "id": "2c3f4913", + "metadata": {}, + "source": [ + "## generate output path" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c36625e8", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "outputPath = os.path.join(os.path.abspath(\".\"), \"output_\" + str(maxX) + \"_res_\" + str(resX) + \"_x_\" + str(resY) + \"/\")\n", + "\n", + "if not os.path.exists(outputPath):\n", + " os.makedirs(outputPath)\n", + "\n", + "os.chdir(outputPath)\n", + "\n", + "delta_timestep = 1.\t\t\t\t\t\t# in years, used in the main loop\n", + "# after how many timesteps do we need new figures?\n", + "update_figures_after_n_timesteps = 1\n", + "number_of_deformation_lines = 11\n", + "\n", + "number_of_deformation_points = 50000\n", + "distance_between_deformation_lines = maxY / (number_of_deformation_lines + 1)\n", + "\n", + "cell_height = maxY / resY\n", + "cell_width = maxX / resX" + ] + }, + { + "cell_type": "markdown", + "id": "f2e7b6a3", + "metadata": {}, + "source": [ + "## Mesh and mesh variables" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9c9afc20", + "metadata": {}, + "outputs": [], + "source": [ + "elementType = \"Q1/dQ0\"\n", + "#elementType = \"Q2/dQ1\"\n", + "#elementType = \"Q1/dPc1\"\n", + "#elementType = \"Q2/dPc1\"\n", + "\n", + "mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType),\n", + " elementRes=(resX, resY),\n", + " minCoord=(minX, minY),\n", + " maxCoord=(maxX, maxY),\n", + " periodic=[True, False])\n", + "\n", + "submesh = mesh.subMesh\n", + "\n", + "# save the mesh\n", + "# mesh.save(outputPath + \"mesh.h5\")\n", + "\n", + "velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim)\n", + "#pressureField = uw.mesh.MeshVariable(mesh=mesh.subMesh, nodeDofCount=1)\n", + "pressureField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1)\n", + "\n", + "viscosityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1)\n", + "\n", + "strainRateField = mesh.add_variable(nodeDofCount=1)\n", + "\n", + "#pressureField.data[:] = 0.\n", + "velocityField.data[:] = [0., 0.]\n", + "\n", + "# Initialise the 'materialVariable' data to represent different materials.\n", + "materialA = 0 \t# accommodation layer, a.k.a. Sticky Air\n", + "materialV = 1 \t# ice, isotropic\n", + "materialR = 2 # rock\n", + "materialT = 5 # test material in order to test eg interface detection\n", + "\n", + "coord = fn.input()\n", + "\n", + "z_bed_function = surface_height - average_bedthickness + amplitude * fn.math.sin(omega * coord[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "25dddca0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# # Define the ice-rock / ice-air interface \n", + "\n", + "botSet = mesh.specialSets['Bottom_VertexSet']\n", + "topSet = mesh.specialSets['Top_VertexSet']\n", + "\n", + "dx = (maxX - minX) / resX\n", + "iceRockInterface = []\n", + "iceAirInterface = []\n", + "\n", + "dx = (maxX - minX) / resX\n", + "\n", + "for index in range(resX+1):\n", + " \n", + " start_x = dx * index\n", + "\n", + " interface_y = surface_height - average_bedthickness + amplitude * np.sin(start_x * (np.pi * 2.) / (maxX-minX) )\n", + " \n", + " #ind = np.where(abs(mesh.data[:,0] - start_x) < 0.01*dx)\n", + " iceRockInterface.append([start_x, interface_y])\n", + " iceAirInterface.append([start_x, maxY])\n", + "\n", + "\n", + "# # Deform mesh to be almost structurally conforming\n", + "\n", + "# In[15]:\n", + "\n", + "\n", + "def mesh_deform(section,fixPoint,mi):\n", + " \n", + " # fixPoint: the position to be refined\n", + " # mi: representing the gradient of mesh resolution; the larger mi, the larger gradient\n", + " # generally, mi ranges from 0.1 to 3, dependnig on the resolution \n", + " \n", + " # note from Till: \n", + " # I normalize it, because then it becomes more clear to me.\n", + " # normalization is not strictly necessary\n", + " normalize = maxY - minY\n", + "\n", + " section /= normalize\n", + " fixPoint /= normalize\n", + "\n", + " for index in range(len(section)):\n", + " \n", + " maxCoord = np.max(section)\n", + " minCoord = np.min(section)\n", + " \n", + " if section[index] < fixPoint:\n", + " zz_sqrt = (fixPoint - section[index])**mi\n", + " zz_sqrt_max = (fixPoint - minCoord)**mi\n", + " section[index] = fixPoint - (fixPoint - section[index]) * zz_sqrt / zz_sqrt_max\n", + "\n", + " if section[index] > fixPoint:\n", + " zz_sqrt = (section[index] - fixPoint)**mi\n", + " zz_sqrt_max = (maxCoord - fixPoint)**mi\n", + " section[index] = fixPoint + (section[index] - fixPoint) * zz_sqrt/zz_sqrt_max \n", + " \n", + " return (section * normalize)\n", + "\n", + "dx = (maxX - minX) / resX\n", + "\n", + "\n", + "if deform_mesh:\n", + " \n", + " with mesh.deform_mesh():\n", + "\n", + " for index in range(resX+1): \n", + "\n", + " start_x = dx * index\n", + "\n", + " interface_y = surface_height - average_bedthickness + amplitude * np.sin(start_x * (np.pi * 2.) / (maxX-minX) )\n", + "\n", + " #print (start_x,interface_y)\n", + " #lx.append(start_x)\n", + " #ly.append(interface_y)\n", + "\n", + " #ind = np.where(abs(mesh.data[:,0] - start_x) < 0.01*dx)\n", + " ind = np.where(abs(mesh.data[:,0] - start_x) < 0.01*dx)\n", + "\n", + " mesh.data[ind[0],1] = mesh_deform(mesh.data[ind[0],1], interface_y, 0.25)\n", + "\n", + "# visualise the result\n", + "figMesh = vis.Figure(figsize=(1200,600))\n", + "figMesh.append( vis.objects.Mesh(mesh) )\n", + "figMesh.save_image(\"mesh_postdeform.png\")\n", + "figMesh.show()" + ] + }, + { + "cell_type": "markdown", + "id": "6a5181b7", + "metadata": {}, + "source": [ + "## Deform mesh to a perfect body fit mesh" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "d6f0a873", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# visualise the result\n", + "def mesh_deform_Ind(section,fixPoint_index,fixPoint,mi):\n", + " \n", + " section[int(fixPoint_index)] = fixPoint\n", + " seqN = len(section)\n", + " \n", + " # fixPoint_index (int): specify the index of the section to be at the place need to be refined\n", + " # fixPoint: the position to be refined\n", + " # mi: representing the gradient of mesh resolution; the larger mi, the larger gradient\n", + " for index in range(len(section)):\n", + " \n", + " maxCoord = np.max(section)\n", + " minCoord = np.min(section)\n", + " \n", + " if index < fixPoint_index:\n", + " section[index] = minCoord + index*(fixPoint-minCoord)/fixPoint_index \n", + " zz_sqrt = (fixPoint-section[index])**mi\n", + " zz_sqrt_max = (fixPoint-minCoord)**mi\n", + " section[index] = fixPoint-(fixPoint-section[index])*zz_sqrt/zz_sqrt_max\n", + "\n", + " if index > fixPoint_index:\n", + " section[index] = fixPoint + (index-fixPoint_index)*(maxCoord-fixPoint)/(seqN-fixPoint_index-1)\n", + " zz_sqrt = (section[index]-fixPoint)**mi\n", + " zz_sqrt_max = (maxCoord-fixPoint)**mi\n", + " section[index] =fixPoint+(section[index]-fixPoint)*zz_sqrt/zz_sqrt_max \n", + " \n", + " return (section)\n", + "\n", + "if (perfect_mesh):\n", + " \n", + " with mesh.deform_mesh():\n", + " \n", + " for index in range(resX+1): \n", + " start_x = dx * index\n", + " \n", + " interface_y = surface_height - average_bedthickness + amplitude * np.sin(start_x * (np.pi * 2.) / (maxX-minX) )\n", + " \n", + " ind = np.where(abs(mesh.data[:,0]-start_x)<0.01*dx)\n", + " \n", + " mesh.data[ind[0],1] = mesh_deform_Ind(mesh.data[ind[0],1],resY/2,interface_y,0.2)\n", + " # make the swarm belong the element that is the same as the in the regular mesh\n", + " \n", + " # visualise the result\n", + " figMesh = vis.Figure(figsize=(1200,600))\n", + " figMesh.append( vis.objects.Mesh(mesh) )\n", + " figMesh.save_image(\"mesh_deform_default_swarm.png\")\n", + " figMesh.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "80646580", + "metadata": {}, + "outputs": [], + "source": [ + "part_per_cell = 30\n", + "swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True)\n", + "\n", + "#swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm, particlesPerCell=part_per_cell)\n", + "swarmLayout = uw.swarm.layouts.PerCellGaussLayout( swarm=swarm, gaussPointCount=5 )\n", + "\n", + "swarm.populate_using_layout(layout=swarmLayout)\n", + "\n", + "measurementSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True)\n", + "\n", + "# create pop control object\n", + "pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell)\n", + "pop_control2 = uw.swarm.PopulationControl(measurementSwarm)\n", + "\n", + "# ### Create a particle advection system\n", + "#\n", + "# Note that we need to set up one advector systems for each particle swarm (our global swarm and a separate one if we add passive tracers).\n", + "advector1 = uw.systems.SwarmAdvector(swarm=swarm,velocityField=velocityField, order=2)\n", + "advector2 = uw.systems.SwarmAdvector(swarm=measurementSwarm, velocityField=velocityField, order=2)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "497bd34a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Tracking different materials\n", + "\n", + "materialVariable = swarm.add_variable(dataType=\"int\", count=1)\n", + "\n", + "numbMeasurementPoints = resX + 1\n", + "xloc = np.linspace(0, maxX, numbMeasurementPoints).reshape(-1,1)\n", + "yloc = (surface_height - average_bedthickness + amplitude * np.sin(omega * xloc)).reshape(-1,1)\n", + "xycoor = np.concatenate((xloc,yloc),axis = 1)\n", + "\n", + "measurementSwarm.add_particles_with_coordinates(xycoor)\n", + "\n", + "particleDensity = swarm.add_variable(dataType=\"double\", count=1)\n", + "particleDensity.data[:] = 0.0\n", + "\n", + "coord = fn.input()\n", + "\n", + "conditions = [(coord[1] > surface_height, materialA),\n", + " (coord[1] < z_bed_function, materialR),\n", + " (True, materialV)]\n", + "\n", + "materialVariable.data[:] = fn.branching.conditional(conditions).evaluate(swarm)\n", + "\n", + "#pyplot.plot(measurementSwarm.data[:,0], measurementSwarm.data[:,1], color='black')\n", + "\n", + "figMesh = vis.Figure(figsize=(1200,600))\n", + "figMesh.append( vis.objects.Mesh(mesh) )\n", + "figMesh.append( vis.objects.Points( swarm, materialVariable, pointSize=10.0 ) )\n", + "figMesh.save_image(\"mesh_deform.png\")\n", + "figMesh.show()" + ] + }, + { + "cell_type": "markdown", + "id": "1a4b03d9", + "metadata": {}, + "source": [ + "## Model viscosity" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "f407ff7a", + "metadata": {}, + "outputs": [], + "source": [ + "strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient)\n", + "strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor)\n", + "\n", + "minViscosityIceFn = fn.misc.constant(1e+10 / 3.1536e7)\n", + "maxViscosityIceFn = fn.misc.constant(1e+15 / 3.1536e7)\n", + "\n", + "viscosityFnAir = fn.misc.constant(1e6 / 3.1536e7)\n", + "viscosityFnRock = fn.misc.constant(1e22 / 3.1536e7)\n", + "\n", + "viscosityFnIceBase = 0.5 * A ** (-1./n) * (strainRate_2ndInvariantFn**((1.-n) / float(n)))\n", + "viscosityFnIce = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn)\n", + "\n", + "viscosityMap = {\n", + " materialV: viscosityFnIce,\n", + " materialA: viscosityFnAir,\n", + " materialR: viscosityFnRock,\n", + " }\n", + "\n", + "viscosityFn = fn.branching.map( fn_key=materialVariable, mapping=viscosityMap )\n", + "\n", + "logViscosityFn = fn.math.log10( fn.misc.max( fn.misc.min( viscosityFnIceBase, viscosityFnRock ), viscosityFnAir ) )" + ] + }, + { + "cell_type": "markdown", + "id": "b3817a13", + "metadata": {}, + "source": [ + "## Bouyance force " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "27946c8d", + "metadata": {}, + "outputs": [], + "source": [ + "devStressFn = 2.0 * viscosityFn * strainRateTensor\n", + "shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0\n", + "\n", + "densityFnAir = fn.misc.constant( 0. )\n", + "densityFnIce = fn.misc.constant( ice_density )\n", + "densityFnRock = fn.misc.constant( 2700. )\n", + "\n", + "densityMap = {\n", + " materialA: densityFnAir,\n", + " materialV: densityFnIce,\n", + " materialR: densityFnRock\n", + " }\n", + "\n", + "densityFn = fn.branching.map(fn_key=materialVariable, mapping=densityMap)\n", + "\n", + "particleDensity.data[:] = densityFn.evaluate(swarm)\n", + "\n", + "surf_inclination = 0.5 * np.pi / 180. # 0.1 = Experiment D, 0.5 = Experiment B\n", + "#surf_inclination = 0.\n", + "z_hat = (math.sin(surf_inclination), - math.cos(surf_inclination))\n", + "#z_hat = (0.00872653549, -0.99996192306417128874)\n", + "\n", + "buoyancyFn = densityFn * z_hat * 9.81" + ] + }, + { + "cell_type": "markdown", + "id": "5c1f06d4", + "metadata": {}, + "source": [ + "## Solver and boundary conditions" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "de8090e4", + "metadata": {}, + "outputs": [], + "source": [ + "iWalls = mesh.specialSets[\"MinI_VertexSet\"] + mesh.specialSets[\"MaxI_VertexSet\"]\n", + "jWalls = mesh.specialSets[\"MinJ_VertexSet\"] + mesh.specialSets[\"MaxJ_VertexSet\"]\n", + "base = mesh.specialSets[\"MinJ_VertexSet\"]\n", + "top = mesh.specialSets[\"MaxJ_VertexSet\"]\n", + "\n", + "velocityField.data[:] = [0., 0.]\n", + "\n", + "leftSet = mesh.specialSets['Left_VertexSet']\n", + "rightSet = mesh.specialSets['Right_VertexSet']\n", + "\n", + "### Dirichlet\n", + "condition1 = uw.conditions.DirichletCondition(variable=velocityField,indexSetsPerDof=(botSet, botSet))\n", + "\n", + "velocityField.data[:] = [0., 0.]\n", + "\n", + "stokes = uw.systems.Stokes(\n", + " velocityField=velocityField,\n", + " pressureField=pressureField,\n", + " voronoi_swarm=swarm,\n", + " conditions=[\n", + " condition1,\n", + " ],\n", + " fn_viscosity=viscosityFn,\n", + " fn_bodyforce=buoyancyFn,\n", + ")\n", + "\n", + "solver = uw.systems.Solver(stokes)\n", + "\n", + "#solver.set_inner_method(\"lu\")\n", + "#solver.set_inner_method(\"superlu\")\n", + "solver.set_inner_method(\"mumps\")\n", + "# solver.set_inner_method(\"superludist\")\n", + "# solver.set_inner_method(\"mg\")\n", + "#solver.set_inner_method(\"nomg\")\n", + "\n", + "# solver.set_penalty(1.0e10) # higher penalty = larger stability\n", + "# solver.options.scr.ksp_rtol = 1.0e-3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b671d44a", + "metadata": {}, + "outputs": [], + "source": [ + "# nl_tol = 2.e1\n", + "nl_tol = 5.e-3\n", + "\n", + "surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=top)\n", + "surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=top)\n", + "\n", + "def calibrate_pressure():\n", + "\n", + " global pressureField\n", + " global surfaceArea\n", + " global surfacePressureIntegral\n", + "\n", + " (area,) = surfaceArea.evaluate()\n", + " (p0,) = surfacePressureIntegral.evaluate() \n", + " pressureField.data[:] -= p0 / area\n", + "\n", + " print (f'Calibration pressure {p0 / area}')\n", + "\n", + "# test it out\n", + "try:\n", + " exec_time = time.time()\n", + " # solver.solve(nonLinearIterate=True, nonLinearTolerance=nl_tol, callback_post_solve=calibrate_pressure)\n", + " solver.solve(nonLinearIterate=True, callback_post_solve=calibrate_pressure)\n", + " # solver.solve(nonLinearIterate=True)\n", + " exec_time = time.time() - exec_time\n", + "\n", + " # print time to a file\n", + " with open('../time.txt', 'a') as f:\n", + " f.write('length,' + str(maxX) + ',x_res:,' + str(resX) + ',y_res:,' + str(resY) + ',time in secs:,' + str(exec_time) + '\\n')\n", + " \n", + " # print full stats to a file\n", + " original_stdout = sys.stdout # Save a reference to the original standard output\n", + " \n", + " with open('../stats_' + \"output_\" + str(maxX) + \"_res_\" + str(resX) + '_x_' + str(resY) + '.txt', 'w') as f:\n", + " sys.stdout = f # Change the standard output to the file we created.\n", + " solver.print_stats()\n", + " sys.stdout = original_stdout # Reset the standard output to its original value\n", + " \n", + " solver.print_stats()\n", + "except:\n", + " print(\"Solver died early..\")\n", + " exit(0)\n", + "\n", + "\n", + "# # Output\n", + "\n", + "# In[48]:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1cd2dac8", + "metadata": {}, + "outputs": [], + "source": [ + "meshStressTensor = uw.mesh.MeshVariable(mesh, 3 )\n", + "projectorStress = uw.utils.MeshVariable_Projection( meshStressTensor, devStressFn, type=0 )\n", + "projectorStress.solve()\n", + "\n", + "## correct the pressure\n", + "meshCorrectedPressure = uw.mesh.MeshVariable(mesh, 1 )\n", + "meshSecondCorrectedPressure = mesh.add_variable( 1 )\n", + "\n", + "## a) from the pressureField\n", + "meshCorrectedPress = uw.utils.MeshVariable_Projection( meshCorrectedPressure, pressureField, type=0 )\n", + "meshCorrectedPress.solve()\n", + "\n", + "## b) from the stranirate tensor\n", + "pressureFn = (strainRateTensor[0] + strainRateTensor[1]) * viscosityFn\n", + "meshSecondCorrectedPress = uw.utils.MeshVariable_Projection( meshSecondCorrectedPressure, pressureFn, type=1 )\n", + "meshSecondCorrectedPress.solve()\n", + "\n", + "## shear stress as saved to disk\n", + "shearStressFn = 2.0 * viscosityFn * strainRateTensor[2]\n", + "meshShearStress = mesh.add_variable( 1 )\n", + "\n", + "projectorStress = uw.utils.MeshVariable_Projection( meshShearStress, shearStressFn, type=0 )\n", + "projectorStress.solve()\n", + "\n", + "## second invariant of stress as saved to disk\n", + "secInvStressFn = 2.0 * viscosityFn * strainRate_2ndInvariantFn\n", + "secInvStress = mesh.add_variable( 1 )\n", + "\n", + "projectorStress = uw.utils.MeshVariable_Projection( secInvStress, secInvStressFn, type=0 )\n", + "projectorStress.solve()\n", + "\n", + "# save to disc\n", + "outputFile = os.path.join(os.path.abspath(\".\"), outputPath + \"output_\" + str(maxX) + \".csv\")\n", + "\n", + "####\n", + "\n", + "x = np.linspace(0, maxX, resX+1)\n", + "interfacex = [item[0] for item in iceRockInterface]\n", + "interfacey = [item[1] for item in iceRockInterface]\n", + "\n", + "airinterfacey = [maxY for item in range(resX + 1)]\n", + "\n", + "iceRockInterface = np.array(iceRockInterface)\n", + "iceAirInterface = np.array(iceAirInterface)\n", + "\n", + "add = 1. * cell_height\n", + "sub = - 1. * cell_height\n", + "\n", + "#add = 5.\n", + "#sub = - 5.\n", + "\n", + "###\n", + "\n", + "shearstress_xy_above = []\n", + "corr_shearstress_xy_above = []\n", + "shearstress_xy_below = []\n", + "corr_shearstress_xy_below = []\n", + "\n", + "for i,j in zip(interfacex,interfacey):\n", + " \n", + " shearstress_xy_above.append(shearStressFn.evaluate((i,j + add))[0][0])\n", + " corr_shearstress_xy_above.append(meshStressTensor.evaluate((i,j + add))[0][2])\n", + " \n", + " shearstress_xy_below.append(shearStressFn.evaluate((i,j + sub))[0][0])\n", + " corr_shearstress_xy_below.append(meshStressTensor.evaluate((i,j + sub))[0][2])\n", + " \n", + "secinvstress_above = []\n", + "corr_secinvstress_above = []\n", + "secinvstress_below = []\n", + "corr_secinvstress_below = []\n", + "\n", + "for i,j in zip(interfacex,interfacey):\n", + " \n", + " secinvstress_above.append(secInvStressFn.evaluate((i,j + add))[0][0])\n", + " corr_secinvstress_above.append(secInvStress.evaluate((i,j + add))[0][0])\n", + " \n", + " secinvstress_below.append(secInvStressFn.evaluate((i,j + sub))[0][0])\n", + " corr_secinvstress_below.append(secInvStress.evaluate((i,j + sub))[0][0])\n", + " \n", + "####\n", + "\n", + "pressure = []\n", + "corr_pressure = []\n", + "for i,j in zip(interfacex,interfacey):\n", + " pressure.append(pressureField.evaluate((i, j + add))[0][0])\n", + " corr_pressure.append(meshCorrectedPressure.evaluate((i, j + add))[0][0])\n", + " \n", + "with open(outputFile, \"w\") as text_file:\n", + "\n", + " text_file.write(\"X,\" + \"Y,\" + \"surf vx,\" + \"surf vy,\" + \"tauxy integr. above,\" + \"tauxy dir. above,\" + \"secinvare integr. above,\" + \"secinvar dir. above,\" + \"tauxy integr. below,\" + \"tauxy dir. below,\" + \"secinvare integr. below,\" + \"secinvar dir. below,\" + \"P integr.,\" + \"P dir.,\" + \"\\n\")\n", + " \n", + " for i in range(0,len(interfacex)):\n", + "\n", + " textline = str(interfacex[i]) + \",\" + str(interfacey[i]) + \",\" + str(velocityField.evaluate((interfacex[i], airinterfacey[i]))[0][0]) + \",\" + str(velocityField.evaluate((interfacex[i], airinterfacey[i]))[0][1]) + \",\" + str(corr_shearstress_xy_above[i]) + \",\" + str(shearstress_xy_above[i]) + \",\" + str(corr_secinvstress_above[i]) + \",\" + str(secinvstress_above[i]) + \",\" + str(corr_shearstress_xy_below[i]) + \",\" + str(shearstress_xy_below[i]) + \",\" + str(corr_secinvstress_below[i]) + \",\" + str(secinvstress_below[i]) + \",\" + str(corr_pressure[i]) + \",\" + str(pressure[i]) + \"\\n\"\n", + " \n", + " text_file.write(textline)\n", + "\n", + "# In[116]:\n", + "\n", + "# plot saved files\n", + "\n", + "outputFile = outputPath + \"output_\" + str(maxX) + \".csv\"\n", + "a = np.loadtxt(open(outputFile, \"rb\"), delimiter=\",\", skiprows=1)\n", + "a = a.T\n", + "\n", + "print (\"topo\")\n", + "pyplot.scatter (a[0], a[1])\n", + "yhat = savgol_filter(a[1], 13, 7)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"topo.png\")\n", + "\n", + "print (\"top x vel\")\n", + "pyplot.scatter (a[0], a[2])\n", + "yhat = savgol_filter(a[2], 13, 7)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"top x vel.png\")\n", + "\n", + "print (\"top y vel\")\n", + "pyplot.scatter (a[0], a[3])\n", + "yhat = savgol_filter(a[3], 13, 9)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"top y vel.png\")\n", + "\n", + "print (\"top total vel\")\n", + "pyplot.scatter (a[0], np.sqrt(a[3]**2 + a[2]**2))\n", + "yhat = savgol_filter(np.sqrt(a[3]**2 + a[2]**2), 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"top total vel.png\")\n", + "\n", + "print (\"tau integr. above\")\n", + "pyplot.scatter (a[0], a[4])\n", + "yhat = savgol_filter(a[4], 13, 4)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"tau integr. above.png\")\n", + "\n", + "print (\"tau integr. below\")\n", + "pyplot.scatter (a[0], a[8])\n", + "yhat = savgol_filter(a[8], 13, 4)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"tau integr. below.png\")\n", + "\n", + "print (\"tau dir. above\")\n", + "pyplot.scatter (a[0], a[5])\n", + "yhat = savgol_filter(a[5], 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"tau dir. above.png\")\n", + "\n", + "print (\"tau dir. below\")\n", + "pyplot.scatter (a[0], a[9])\n", + "yhat = savgol_filter(a[9], 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"tau dir. below.png\")\n", + "\n", + "print (\"sec inv integr. above\")\n", + "pyplot.scatter (a[0], a[6])\n", + "yhat = savgol_filter(a[6], 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"sec inv integr. above.png\")\n", + "\n", + "print (\"sec inv integr. below\")\n", + "pyplot.scatter (a[0], a[10])\n", + "yhat = savgol_filter(a[10], 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"sec inv integr. below.png\")\n", + "\n", + "print (\"sec inv dir. above\")\n", + "pyplot.scatter (a[0], a[7])\n", + "yhat = savgol_filter(a[7], 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"sec inv dir. above.png\")\n", + "\n", + "print (\"sec inv dir. below\")\n", + "pyplot.scatter (a[0], a[11])\n", + "yhat = savgol_filter(a[11], 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"sec inv dir. below.png\")\n", + "\n", + "print (\"basal pressure integr.\")\n", + "pyplot.scatter (a[0], a[12])\n", + "yhat = savgol_filter(a[12], 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"basal pressure integr.png\")\n", + "\n", + "print (\"basal pressure dir.\")\n", + "pyplot.scatter (a[0], a[13])\n", + "yhat = savgol_filter(a[13], 13, 5)\n", + "pyplot.plot(a[0], yhat, color='red')\n", + "pyplot.show()\n", + "pyplot.savefig(\"basal pressure dir.png\")\n", + "\n", + "\n", + "# In[ ]:\n", + "\n", + "\n", + "# plot figures\n", + "\n", + "figinflow = vis.Figure(figsize=(1800,500), title=\"free slip with in/out flow\")\n", + "figinflow.append(vis.objects.VectorArrows(mesh, velocityField))\n", + "figinflow.append(vis.objects.Surface(mesh, uw.function.math.dot(velocityField,velocityField), colours=\"gebco\"))\n", + "figinflow.save_image(outputPath + \"velocity_\" + str(maxX) + \".png\")\n", + "figinflow.show()\n", + "\n", + "figMaterial = vis.Figure(figsize=(1800, 500), title=\"Material\")\n", + "figMaterial.append(vis.objects.Points( swarm, materialVariable, pointSize=1.0))\n", + "figMaterial.append( vis.objects.Mesh(mesh) )\n", + "figMaterial.save_image(outputPath + \"material_\" + str(maxX) + \".png\")\n", + "figMaterial.show()\n", + "\n", + "figDensity = vis.Figure(figsize=(1800, 500), title=\"Density\")\n", + "figDensity.append(vis.objects.Points( swarm, particleDensity, pointSize=1.0))\n", + "figDensity.save_image(outputPath + \"density_\" + str(maxX) + \".png\")\n", + "figDensity.show()\n", + "\n", + "figViscosity = vis.Figure(figsize=(1800, 500), title=\"viscosity\")\n", + "figViscosity.append(vis.objects.Surface(mesh, logViscosityFn))\n", + "figViscosity.save_image(outputPath + \"logviscosity_\" + str(maxX) + \".png\")\n", + "figViscosity.show()\n", + "\n", + "figPressure = vis.Figure(figsize=(1800, 500), title=\"pressure\")\n", + "figPressure.append(vis.objects.Surface(mesh, pressureField))\n", + "figPressure.save_image(outputPath + \"pressure_\" + str(maxX) + \".png\")\n", + "figPressure.show()\n", + "\n", + "figShearStress = vis.Figure(figsize=(1800, 500), title=\"corr_shearstress_xy\")\n", + "figShearStress.append(vis.objects.Surface(mesh, meshShearStress))\n", + "figShearStress.save_image(outputPath + \"corr_shearstress_xy\" + str(maxX) + \".png\")\n", + "figShearStress.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cde0535d", + "metadata": {}, + "source": [ + "\n", + "## finally save meshvars, swarmvars, xdmf vars" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fda42da2", + "metadata": {}, + "outputs": [], + "source": [ + "# In[ ]:\n", + "\n", + "\n", + "xdmf_info_mesh = mesh.save('mesh.h5')\n", + "xdmf_info_meshVelocityField = velocityField.save('meshVelocityField.h5')\n", + "xdmf_info_meshShearStress = meshShearStress.save('meshShearStress.h5')\n", + "xdmf_info_meshCorrectedPressure = meshCorrectedPressure.save('meshCorrectedPressure.h5')\n", + "\n", + "# swarm\n", + "xdmf_info_swarm = swarm.save('swarm.h5')\n", + "xdmf_info_swarmMaterialVariable = materialVariable.save('swarmMaterialVariable.h5')\n", + "\n", + "# xdmf mesh\n", + "velocityField.xdmf('meshVelocityField.xdmf', xdmf_info_meshVelocityField, \"velocityField\", xdmf_info_mesh, \"TheMesh\", modeltime=0.0)\n", + "meshShearStress.xdmf('meshShearStress.xdmf', xdmf_info_meshShearStress, \"meshShearStress\", xdmf_info_mesh, \"TheMesh\", modeltime=0.0)\n", + "meshCorrectedPressure.xdmf('meshCorrectedPressure.xdmf', xdmf_info_meshCorrectedPressure, \"correctedPressureField\", xdmf_info_mesh, \"TheMesh\", modeltime=0.0)\n", + "\n", + "# xdmf swarm\n", + "materialVariable.xdmf('swarmMaterialVariable.xdmf', xdmf_info_swarmMaterialVariable, \"material\", xdmf_info_swarm, \"TheSwarm\", modeltime=0.0)\n", + "\n", + "\n", + "# In[ ]:" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "underworld", + "language": "python", + "name": "underworld" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/model_code_inputs/Exp_C-3D.py b/model_code_inputs/Exp_C-3D.py new file mode 100644 index 0000000..c1de081 --- /dev/null +++ b/model_code_inputs/Exp_C-3D.py @@ -0,0 +1,610 @@ +#!/usr/bin/env python +# coding: utf-8 +# %% +## Basic python imports and model settings + +# %% +import underworld.visualisation as vis + +from underworld import function as fn +import underworld as uw + +import matplotlib.pyplot as pyplot +import numpy as np +from scipy.spatial import distance + +import math +import os +import sys + +import time + +from scipy.signal import savgol_filter + +# details of the bottom curve +L = [160, 5, 80, 40, 20, 10] + +# make it command line compatible +if len(sys.argv): + try: + km_index = int(sys.argv[1]) + except: + km_index = 5 + +i = km_index + +systemDim = L[i] + +maxZ = maxX = L[i] * 1000. + +resX = 128 +resY = 48 +resZ = 4 + +omega = 2.0 * np.pi / maxX +alpha = 0.1 / 180. * np.pi # 0.1 = Experiment C + D, 0.5 = Experiment A + B +amplitude = 500. + +surface_height = 1000. + 1000. / (resY-1) + +maxY = surface_height + +minY = minX = minZ = 0. + +g = 9.81 +ice_density = 910. + +A = 1e-16 +n = 3. + +print("resX: " + str(resX) + " resY: " + str(resY) ) + +# generate output path +outputPath = os.path.join(os.path.abspath("."), "output_" + str(maxX) + "_res_" + str(resX) + "_x_" + str(resY) + "_x_" + str(resZ) + "/") + +if not os.path.exists(outputPath): + os.makedirs(outputPath) + +os.chdir(outputPath) + +delta_timestep = 1. # in years, used in the main loop +# after how many timesteps do we need new figures? + +cell_height = maxY / resY +cell_width = maxX / resX +cell_depth = maxZ / resZ + + +# # The mesh + +# %% + + + +elementType = "Q1/dQ0" + +mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType), + elementRes=(resX, resY, resZ), + minCoord=(minX, minY, minZ), + maxCoord=(maxX, maxY, maxZ), + periodic=[True, False, True]) + +submesh = mesh.subMesh + +# save the mesh +# mesh.save(outputPath + "mesh.h5") + +velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +#pressureField = uw.mesh.MeshVariable(mesh=mesh.subMesh, nodeDofCount=1) +pressureField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +viscosityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +strainRateField = mesh.add_variable(nodeDofCount=1) + +#pressureField.data[:] = 0. +velocityField.data[:] = [0., 0., 0.] + + +# # The swarm + +# %% + + +part_per_cell = 500 +swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# Initialise the 'materialVariable' data to represent different materials. +materialV = 0 # ice, isotropic +materialB = 1 # + +swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm, particlesPerCell=part_per_cell) +#swarmLayout = uw.swarm.layouts.PerCellGaussLayout( swarm=swarm, gaussPointCount=5 ) + +swarm.populate_using_layout(layout=swarmLayout) + +#measurementSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# create pop control object +#pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell) +#pop_control2 = uw.swarm.PopulationControl(measurementSwarm) + +# ### Create a particle advection system +# +# Note that we need to set up one advector systems for each particle swarm (our global swarm and a separate one if we add passive tracers). +#advector1 = uw.systems.SwarmAdvector(swarm=swarm, velocityField=velocityField, order=2) +#advector2 = uw.systems.SwarmAdvector(swarm=measurementSwarm, velocityField=velocityField, order=2) + + +# # Definition of basal friction + +# %% + + +coord = fn.input() +beta_square = 1000. + 1000. * fn.math.sin(omega * fn.input()[0]) * fn.math.sin(omega * fn.input()[2]) + 1e-18 +#1000. + 1000. * fn.math.sin(omega * fn.input()[0]) + 1e-18 + + +# # Set the material for the ice-rock interface + +# %% + + +# Tracking different materials + +materialVariable = swarm.add_variable(dataType="int", count=1) + +particleDensity = swarm.add_variable(dataType="double", count=1) +particleDensity.data[:] = ice_density + +coord = fn.input() + +#if(coord[1] <= cell_height): # inside the circle + # materialVariable.data[:] = materialB +conditions = [(coord[1] > cell_height, materialV), + (coord[1] <= cell_height, materialB), + (True, materialV)] + +materialVariable.data[:] = fn.branching.conditional(conditions).evaluate(swarm) +#pyplot.plot(measurementSwarm.data[:,0], measurementSwarm.data[:,1], color='black') + + +# # Boundary conditions + +# %% + + +iWalls = mesh.specialSets["MinI_VertexSet"] + mesh.specialSets["MaxI_VertexSet"] +jWalls = mesh.specialSets["MinJ_VertexSet"] + mesh.specialSets["MaxJ_VertexSet"] +kWalls = mesh.specialSets["MinK_VertexSet"] + mesh.specialSets["MaxK_VertexSet"] + +# Surface points +top = mesh.specialSets["MaxJ_VertexSet"] + +# Basis points +# base = ... +# defined in the mesh_deform_Ind function above + +velocityField.data[:] = [1., 0., 0.] + +leftSet = mesh.specialSets['Left_VertexSet'] +rightSet = mesh.specialSets['Right_VertexSet'] +botSet = mesh.specialSets['Bottom_VertexSet'] + +# Dirichlet +condition = uw.conditions.DirichletCondition(variable = velocityField, indexSetsPerDof=(botSet, botSet, botSet)) + +velocityField.data[:] = [0., 0., 0.] + +#As = 1. / beta_square +#tau_b = maxY * np.sin(alpha) * 9.81 * 910. +#basalVelocityField = mesh.add_variable(1) +#basalVelocityField.data[:] = tau_b / beta_square.evaluate(mesh.data) + + +# # Strainrate + +# %% + + +strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient) +strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor) + + +# # Effective viscosity, density and gravity + +# %% + + +minViscosityIceFn = fn.misc.constant(1e+8 / 31556926) +maxViscosityIceFn = fn.misc.constant(1e+16 / 31556926) + +viscosityFnRock = fn.misc.constant(1e23 / 31556926) + +viscosityFnIceBase = 0.5 * A ** (-1./n) * (strainRate_2ndInvariantFn**((1.-n) / float(n))) +viscosityFnIce = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn) +#viscosityFnIce = fn.misc.constant(2e13 / 31556926) +viscosityFnBase = cell_height * beta_square + +viscosityMap = { + materialV: viscosityFnIce, + materialB: viscosityFnBase, + } + +viscosityFn = fn.branching.map( fn_key=materialVariable, mapping=viscosityMap ) + +densityFnIce = fn.misc.constant( ice_density ) +densityFnRock = fn.misc.constant( 2700. ) +densityFnAir = fn.misc.constant (0.) + +densityMap = { + materialV: densityFnIce, + materialB: densityFnIce, + } + +densityFn = densityFnIce + +surf_inclination = alpha +z_hat = (math.sin(surf_inclination), - math.cos(surf_inclination), 0.) + +buoyancyFn = densityFn * z_hat * 9.81 + + +# %% + + +''' +figMesh = vis.Figure(figsize=(1200,600)) +figMesh.append( vis.objects.Mesh(mesh) ) +figMesh.append( vis.objects.Points( swarm, materialVariable, pointSize=10.0 ) ) +figMesh.save_image("mesh_deform.png") +figMesh.show() +''' + +particleViscosity = swarm.add_variable(dataType="double", count=1) +particleViscosity.data[:] = viscosityFn.evaluate(swarm) + +# example for 3D +figMaterials = vis.Figure(title="Basis") +#figMaterials.append( vis.objects.Mesh(mesh) ) +#figMaterials.append(vis.objects.Points(swarm, coord[1], pointSize=4.0, colourBar=True,)) +figMaterials.append(vis.objects.Points(swarm, particleViscosity, fn_mask=materialVariable, pointSize=4.0, colourBar=True)) +figMaterials.window() + + +# # Stress + +# %% + + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + + +# # Solver + +# %% + + +stokes = uw.systems.Stokes( + velocityField=velocityField, + pressureField=pressureField, + voronoi_swarm=swarm, + conditions=condition, + fn_viscosity=viscosityFn, + fn_bodyforce=buoyancyFn, +) + +solver = uw.systems.Solver (stokes) + +#solver.set_inner_method ("lu") +#solver.set_inner_method ("superlu") +solver.set_inner_method ("mumps") +#solver.set_inner_method ("superludist") +#solver.set_inner_method ("mg") +#solver.set_inner_method ("nomg") + +# solver.set_penalty (1.0e21 / 31556926) # higher penalty = larger stability + +#solver.options.scr.ksp_rtol = 1.0e-3 +solver.set_penalty( 1.e6 ) +nl_tol = 1.e-2 # standard value + +surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=top) +surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=top) + +def calibrate_pressure(): + + global pressureField + global surfaceArea + global surfacePressureIntegral + + (area,) = surfaceArea.evaluate() + (p0,) = surfacePressureIntegral.evaluate() + pressureField.data[:] -= p0 / area + + print (f'Calibration pressure {p0 / area}') + +# test it out +try: + exec_time = time.time() + solver.solve(nonLinearIterate=True, nonLinearTolerance=nl_tol, callback_post_solve=calibrate_pressure) + #solver.solve(nonLinearIterate=True, callback_post_solve=calibrate_pressure) + exec_time = time.time() - exec_time + + # print full stats to a file + solver.print_stats() +except: + print("Solver died early..") + exit(0) + +print (exec_time) + + +# # Shearstress +# +# Stress is a symmetric tensor, and underword can deal with this in the 'underworld.function.tensor'. Call `help(uw.function.tensor)` to get the description! +# +# A symmetric tensor in underworld is stored as a list: +# $$\left[ a_{00}, a_{11}, a_{22}, a_{01}, a_{02}, a_{12} \right]$$ +# +# The elements of the list correspond to the following naming scheme for the elements of a matrix: +# $$ +# \left[ a_{00}, a_{01}, a_{02}, \\ +# a_{01}, a_{11}, a_{12}, \\ +# a_{02}, a_{12}, a_{22} \right] +# $$ +# +# So, if your Stress-function is called 'devStressFn' and returns an underworld-tensor (called $\sigma$ in the following), then you can access the element $a_{22}$ of that tensor by: +# +# devStressFn.evaluate((x,y,z))[0][2] +# +# (the first [0] is needed, because underworld return a list of lists, see below). +# +# The following line will return the value $\sigma_{11}$, corresponding to $a_{11}$ above: +# +# devStressFn.evaluate((3000., 1000., 3000.))[0][1] + +# # Write out surface data + +# %% + + +xpos = np.arange(start=0, stop=int(resX+1)) * maxX / resX +zpos = np.ones(resX+1) * maxZ * 0.25 + +xz = np.array(np.meshgrid(xpos, zpos)).T.reshape(-1,2) + +surf_pos = np.insert(xz, 1, maxY, axis=1 ) +base_pos = np.insert(xz, 1, 0., axis=1 ) + + +# ## New output routine (all points) + +# %% + + +#### Filename +outputFile = os.path.join(os.path.abspath("."), "jla"+"1c"+ str(systemDim).zfill(3) + ".csv") +print(outputFile) + +#### Smooth the stress +meshStressTensor = uw.mesh.MeshVariable(mesh, 6) +projectorStress = uw.utils.MeshVariable_Projection( meshStressTensor, devStressFn, type=0 ) +projectorStress.solve() + +#### Smooth the velocity +meshVelocity = uw.mesh.MeshVariable(mesh, 3) +projectorV = uw.utils.MeshVariable_Projection( meshVelocity, velocityField, type=0 ) +projectorV.solve() + +#### Smooth the pressure +meshP = uw.mesh.MeshVariable(mesh, 1) +projectorP = uw.utils.MeshVariable_Projection( meshP, pressureField, type=0 ) +projectorP.solve() + +#### Points +xpos = np.arange(start=0, stop=int(resX+1)) * maxX / resX +zpos = np.arange(start=0, stop=int(resZ+1)) * maxZ / resZ + +xz = np.array(np.meshgrid(xpos, zpos)).T.reshape(-1,2) + +sub = 1. * cell_height +add = 0. * cell_height + +surf_pos = np.insert(xz, 1, maxY - sub, axis=1 ) +base_pos = np.insert(xz, 1, 0. + add, axis=1 ) + +#### Get the surface velocity +#vxs = meshVelocity.evaluate(surf_pos).transpose()[0] +#vys = meshVelocity.evaluate(surf_pos).transpose()[1] +#vzs = meshVelocity.evaluate(surf_pos).transpose()[2] +vxs = velocityField.evaluate(surf_pos).transpose()[0] +vys = velocityField.evaluate(surf_pos).transpose()[1] +vzs = velocityField.evaluate(surf_pos).transpose()[2] + +vtots = np.sqrt( vxs*vxs + vys*vys + vzs*vzs ) + +#### Get the basal velocity +#vxb = meshVelocity.evaluate(base_pos).transpose()[0] +#vyb = meshVelocity.evaluate(base_pos).transpose()[1] +#vzb = meshVelocity.evaluate(base_pos).transpose()[2] +vxb = velocityField.evaluate(base_pos).transpose()[0] +vyb = velocityField.evaluate(base_pos).transpose()[1] +vzb = velocityField.evaluate(base_pos).transpose()[2] + +vtotb = np.sqrt( vxb*vxb + vyb*vyb + vzb*vzb ) + +#### Get the pressure +#P = meshP.evaluate(base_pos).squeeze() +P = pressureField.evaluate(base_pos).squeeze() + +#### Get the shearstress +sxz = meshStressTensor.evaluate(base_pos).squeeze()[:,3] +#sxz = devStressFn.evaluate(base_pos).squeeze()[:,3] + +sxy = meshStressTensor.evaluate(base_pos).squeeze()[:,4] +#sxz = devStressFn.evaluate(base_pos).squeeze()[:,3] + +#### only indices where z ~ 0.25 +ind = np.where(np.logical_and(xz[:,1] > 0.24 * maxZ , xz[:,1] < 0.26 * maxZ)) + +#### plot pressure from grid / theoretical / difference +print("DeltaP") +#pyplot.plot((maxY - base_ypos[:]) * 9.81 * 910, color='red') +pyplot.plot(P[ind], color='blue') +pyplot.plot( P[ind] - (maxY - base_pos[ind, 1].squeeze()) * 9.81 * 910., color='green') +pyplot.show() + +#### plot vx at surface +print("vxs") +pyplot.plot(vxs[ind], color='red') +pyplot.show() + +### plot shear stress +print("Shear stress") +pyplot.plot(sxz[ind] / 1000., color='red') +pyplot.show() + +#### output to file +with open(outputFile, "w") as text_file: + + for i in range(len(surf_pos)): + + # Ausgabe [x] [y] + textline = str("{:.7f}".format(surf_pos[i, 0] / maxX)) + "\t" + str("{:.7f}".format(surf_pos[i, 2] / maxZ)) + "\t" + + #Ausgabe Geschwindigkeiten Surface[vx] [vy] [vz] + textline += str("{:.7f}".format(vxs[i])) + "\t" + str("{:.7f}".format(vzs[i])) + "\t" + str("{:.7f}".format(vys[i])) + "\t" + + #Ausgabe Geschwindigkeiten Basis [vx] [vy] + textline += str("{:.7f}".format(vxb[i])) + "\t" + str("{:.7f}".format(vzb[i])) + "\t" + + # Scherspannung Basis Tensoren [Txz] [Tyz] + textline += str("{:.7f}".format(sxz[i] / 1000.)) + "\t" + str("{:.7f}".format(sxy[i] / 1000.)) + "\t" + + # Ausgabe delta p + textline += str("{:.7f}".format( (P[i] - float((maxY - base_pos[i, 1]) * 9.81 * 910 )) / 1000)) + "\n" + + text_file.write(textline) + + + +# ## old output routine (usually to be commented out) + +# %% + + +''' +#### Filename +outputFile = os.path.join(os.path.abspath("."), "jla"+"1c"+ str(systemDim).zfill(3) + ".csv") +print(outputFile) + +#### Smooth the stress +meshStressTensor = uw.mesh.MeshVariable(mesh, 6) +projectorStress = uw.utils.MeshVariable_Projection( meshStressTensor, devStressFn, type=0 ) +projectorStress.solve() + +#### Smooth the velocity +meshVelocity = uw.mesh.MeshVariable(mesh, 3) +projectorV = uw.utils.MeshVariable_Projection( meshVelocity, velocityField, type=0 ) +projectorV.solve() + +#### Smooth the pressure +meshP = uw.mesh.MeshVariable(mesh, 1) +projectorP = uw.utils.MeshVariable_Projection( meshP, pressureField, type=0 ) +projectorP.solve() + +#### Points +surf_xpos = base_xpos = np.arange(start=0, stop=int(resX+1)) * maxX / resX +surf_zpos = base_zpos = np.ones(resX+1) * maxZ * 0.25 + +base_ypos = np.zeros(resX+1) +surf_ypos = np.ones(resX+1) * maxY + +base_ypos += 0. * cell_height +surf_ypos -= .1 * cell_height + +base_pos = np.column_stack( (base_xpos, base_ypos, base_zpos) ) +surf_pos = np.column_stack( (surf_xpos, surf_ypos, surf_zpos) ) + +#### Get the surface velocity +#vxs = meshVelocity.evaluate(surf_pos).transpose()[0] +#vys = meshVelocity.evaluate(surf_pos).transpose()[1] +#vzs = meshVelocity.evaluate(surf_pos).transpose()[2] +vxs = velocityField.evaluate(surf_pos).transpose()[0] +vys = velocityField.evaluate(surf_pos).transpose()[1] +vzs = velocityField.evaluate(surf_pos).transpose()[2] + +vtots = np.sqrt( vxs*vxs + vys*vys + vzs*vzs ) + +#### Get the basal velocity +#vxb = meshVelocity.evaluate(base_pos).transpose()[0] +#vyb = meshVelocity.evaluate(base_pos).transpose()[1] +#vzb = meshVelocity.evaluate(base_pos).transpose()[2] +vxb = velocityField.evaluate(base_pos).transpose()[0] +vyb = velocityField.evaluate(base_pos).transpose()[1] +vzb = velocityField.evaluate(base_pos).transpose()[2] + +vtotb = np.sqrt( vxb*vxb + vyb*vyb + vzb*vzb ) + +#### Get the pressure +#P = meshP.evaluate(base_pos).squeeze() +P = pressureField.evaluate(base_pos).squeeze() + +#### Get the shearstress +sxz = meshStressTensor.evaluate(base_pos).squeeze()[:,3] +#sxz = devStressFn.evaluate(base_pos).squeeze()[:,3] + +sxy = meshStressTensor.evaluate(base_pos).squeeze()[:,4] +#sxz = devStressFn.evaluate(base_pos).squeeze()[:,3] + +#### plot pressure from grid / theoretical / difference +print("DeltaP") +#pyplot.plot((maxY - base_ypos[:]) * 9.81 * 910, color='red') +pyplot.plot(P, color='blue') +pyplot.plot( P - (maxY - base_ypos) * 9.81 * 910., color='green') +pyplot.show() + +#### plot vx at surface +print("vxs") +pyplot.plot(vxs, color='red') +pyplot.show() + +### plot shear stress +print("Shear stress") +pyplot.plot(sxz / 1000., color='red') +pyplot.show() + +#### output to file +with open(outputFile, "w") as text_file: + + for i in range(0, resX+1): + + # Ausgabe [x] [y] + textline = str("{:.7f}".format(surf_pos[i, 0] / maxX)) + "\t" \ + + str("{:.7f}".format(surf_pos[i, 2] / maxZ)) + "\t" + + #Ausgabe Geschwindigkeiten Surface[vx] [vy] [vz] + textline += str("{:.7f}".format(vxs[i])) + "\t" + str("{:.7f}".format(vzs[i])) \ + + "\t" + str("{:.7f}".format(vys[i])) + "\t" + + #Ausgabe Geschwindigkeiten Basis [vx] [vy] + textline += str("{:.7f}".format(vxb[i])) + "\t" + str("{:.7f}".format(vzb[i])) + "\t" + + # Scherspannung Basis Tensoren [Txz] [Tyz] + textline += str("{:.7f}".format(sxz[i] / 1000.)) + "\t" + str("{:.7f}".format(sxy[i] / 1000.)) + "\t" + + # Ausgabe delta p + textline += str("{:.7f}".format(float(P[i]) - float((maxY - base_pos[i, 1]) * 9.81 * 910 / 1000))) + "\n" + + text_file.write(textline) +''' + + +# %% + + + + diff --git a/model_code_inputs/Exp_D-2D.py b/model_code_inputs/Exp_D-2D.py new file mode 100644 index 0000000..2c1bbfb --- /dev/null +++ b/model_code_inputs/Exp_D-2D.py @@ -0,0 +1,466 @@ +#!/usr/bin/env python +# coding: utf-8 + +# # Basic python imports and model settings + +# In[ ]: + + +import underworld.visualisation as vis + +from underworld import function as fn +import underworld as uw + +import matplotlib.pyplot as pyplot +import numpy as np +from scipy.spatial import distance + +import math +import os +import sys + +import time as ti + +from scipy.signal import savgol_filter + +# details of the bottom curve +# details of the bottom curve +# details of the bottom curve +L = [160, 80, 40, 20, 10, 5] + +# make it command line compatible +if len(sys.argv): + try: + km_index = int(sys.argv[1]) + except: + km_index = 5 + +i = km_index + +maxX = L[i] * 1000. +min_bed_height = 0. # we want exactly 0 m of rock beneath the ice + +maxY = 1000. + +omega = 2. * np.pi / maxX +alpha = 0.1 / 180. * np.pi + +beta_square = 1000. + 1000. * fn.math.sin(omega * fn.input()[0]) + 1e-18 +As = 1. / beta_square +tau_b = maxY * np.sin(alpha) * 9.81 * 910. + +g = 9.81 +ice_density = 910. + +A = 1e-16 +n = 3. + +resY = 75 +resX = 375 + +print("resX: " + str(resX) + " resY: " + str(resY)) + +# generate output path +outputPath = os.path.join(os.path.abspath("."), "output_" + str(maxX) + "/") +if not os.path.exists(outputPath): + os.makedirs(outputPath) + +os.chdir(outputPath) + +delta_timestep = 1. # in years, used in the main loop +# after how many timesteps do we need new figures? +update_figures_after_n_timesteps = 1 +number_of_deformation_lines = 11 + +number_of_deformation_points = 50000 +distance_between_deformation_lines = maxY / (number_of_deformation_lines + 1)# + +cell_height = maxY / resY +cell_width = maxX / resX + + +# # Mesh + mesh variables + +# In[3]: + + +elementType = "Q1/dQ0" + +mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType), + elementRes=(resX, resY), + minCoord=(0., 0.), + maxCoord=(maxX, maxY), + periodic=[True, False]) + +submesh = mesh.subMesh + +# save the mesh +# mesh.save(outputPath + "mesh.h5") + +velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +pressureField = uw.mesh.MeshVariable(mesh=mesh.subMesh, nodeDofCount=1) + +viscosityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +materialField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +strainRateField = mesh.add_variable(1) +basalVelocityField = mesh.add_variable(1) + +pressureField.data[:] = 0. +velocityField.data[:] = [0., 0.] +materialField.data[:] = [0] +basalVelocityField.data[:] = tau_b / beta_square.evaluate(mesh.data) + +# Initialise the 'materialVariable' data to represent different materials. +materialA = 0 # accommodation layer, a.k.a. Sticky Air +materialV = 1 # ice, isotropic +materialR = 2 # rock +materialT = 5 # test material in order to test eg interface detection +materialB = 6 + +botSet = mesh.specialSets['Bottom_VertexSet'] +topSet = mesh.specialSets['Top_VertexSet'] + + +# # Define the ice-air and ice-rock interface +# +# (which are just the min/max coordinates in this experiment, but I'll keep the commented-out Exp-B version as reference and for more flexibility) + +# In[15]: + + +iceRockInterfaceSet = mesh.add_variable(1) +iceAirInterfaceSet = mesh.add_variable(1) + +iceRockInterfaceSet.data[:] = False +iceAirInterfaceSet.data[:] = False + +iceAirInterfaceSet.data[topSet] = True + +iceRockInterfaceSet.data[:] = False +for i, m in np.ndenumerate(mesh.data[:,1]): + + if m > 0.5*cell_height and m < 1.5*cell_height: + iceRockInterfaceSet.data[i] = True + +# iceRockInterfaceSet = np.where(iceRockInterfaceSet.data[:])[0] +# iceAirInterfaceSet = np.where(iceAirInterfaceSet.data[:])[0] + +l = np.where(iceAirInterfaceSet.data[:])[0] +inds = mesh.data[l,0].argsort() +iceAirInterfaceSet = l[inds] + +l = np.where(iceRockInterfaceSet.data[:])[0] +inds = mesh.data[l,0].argsort() +iceRockInterfaceSet = l[inds] + + +iceAirInterfaceSet = topSet +bottomInterfaceSet = botSet + + +# # Swarm + +# In[5]: + + +part_per_cell = 50 +swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) +swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout( + swarm=swarm, particlesPerCell=part_per_cell) +swarm.populate_using_layout(layout=swarmLayout) + +surfaceSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) +deformationSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# create pop control object +pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell) +pop_control2 = uw.swarm.PopulationControl(surfaceSwarm) +pop_control3 = uw.swarm.PopulationControl(deformationSwarm) + +# ### Create a particle advection system +# +# Note that we need to set up one advector system for each particle swarm (our global swarm and a separate one if we add passive tracers). +advector1 = uw.systems.SwarmAdvector(swarm=swarm,velocityField=velocityField, order=2) +advector2 = uw.systems.SwarmAdvector(swarm=surfaceSwarm, velocityField=velocityField, order=2) +advector3 = uw.systems.SwarmAdvector(swarm=deformationSwarm, velocityField=velocityField, order=2) + +# Tracking different materials + +materialVariable = swarm.add_variable(dataType="int", count=1) + +# passive markers at the surface are inserted whenever 100 m of new snow hav been created in the main loop +deformationPoints = np.array(np.meshgrid(np.linspace(0., maxX, int( + number_of_deformation_points)), np.linspace(0., maxY, number_of_deformation_lines))).T.reshape(-1, 2) +deformationSwarm.add_particles_with_coordinates(deformationPoints) + +surfacePoints = np.zeros((int(number_of_deformation_points), 2)) +surfacePoints[:, 0] = np.linspace(0., maxX, int(number_of_deformation_points)) +surfacePoints[:, 1] = maxY +surfaceSwarm.add_particles_with_coordinates(surfacePoints) + +particleDensity = swarm.add_variable(dataType="double", count=1) +particleDensity.data[:] = 0.0 + +materialVariable.data[:] = materialV +materialVariable.data[botSet] = materialB + +for index, coord in enumerate(swarm.particleCoordinates.data): + if(coord[1] <= cell_height): # inside the circle + materialVariable.data[index] = materialB + +#figMaterial = vis.Figure(figsize=(1800, 500)) +#figMaterial.append(vis.objects.Points( swarm, materialVariable, pointSize=1.0)) +#figMaterial.show() +#figMaterial.save_image("material.png") + + +# # Functions + +# In[6]: + + +strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient) +strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor) + +minViscosityIceFn = fn.misc.constant(1e+10 / 3.1536e7) +maxViscosityIceFn = fn.misc.constant(1e+15 / 3.1536e7) + +viscosityFnAir = fn.misc.constant(1e6 / 3.1536e7) +viscosityFnRock = fn.misc.constant(1e22 / 3.1536e7) + +viscosityFnIceBase = 0.5 * A ** (-1./n) * (strainRate_2ndInvariantFn**((1.-n) / n)) +viscosityFnIce = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn) + +viscosityFnBase = cell_height * beta_square + +viscosityMap = { + materialV: viscosityFnIce, + materialA: viscosityFnAir, + materialR: viscosityFnRock, + materialB: viscosityFnBase, + } + +viscosityFn = fn.branching.map( fn_key=materialVariable, mapping=viscosityMap ) + +logViscosityFn = fn.math.log10( fn.misc.max( fn.misc.min( viscosityFnIceBase, viscosityFnRock ), viscosityFnAir ) ) + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +densityFnAir = fn.misc.constant( 0. ) +densityFnIce = fn.misc.constant( ice_density ) +densityFnRock = fn.misc.constant( 2700. ) + +densityMap = { + materialA: densityFnAir, + materialV: densityFnIce, + materialR: densityFnRock, + materialB: densityFnIce, + } + +densityFn = fn.branching.map(fn_key=materialVariable, mapping=densityMap) + +#particleDensity.data[:] = densityFn.evaluate(swarm) + +particleDensity.data[:] = 910. + +surf_inclination = 0.1 * np.pi / 180. # 0.1 = Experiment D, 0.5 = Experiment B +#surf_inclination = 0. +z_hat = (math.sin(surf_inclination), - math.cos(surf_inclination)) + +buoyancyFn = densityFn * z_hat * 9.81 + + +# # Solver and boundary conditions + +# In[7]: + + +iWalls = mesh.specialSets["MinI_VertexSet"] + mesh.specialSets["MaxI_VertexSet"] +jWalls = mesh.specialSets["MinJ_VertexSet"] + mesh.specialSets["MaxJ_VertexSet"] +base = mesh.specialSets["MinJ_VertexSet"] +top = mesh.specialSets["MaxJ_VertexSet"] + +velocityField.data[:] = [0., 0.] + +botSet = mesh.specialSets['Bottom_VertexSet'] +topSet = mesh.specialSets['Top_VertexSet'] +leftSet = mesh.specialSets['Left_VertexSet'] +rightSet = mesh.specialSets['Right_VertexSet'] + +### Dirichlet +condition1 = uw.conditions.DirichletCondition(variable=velocityField,indexSetsPerDof=(botSet, botSet)) + +velocityField.data[:] = [0., 0.] +#velocityField.data[botSet] = basalVelocityField.data[botSet] + +stokes = uw.systems.Stokes( + velocityField=velocityField, + pressureField=pressureField, + voronoi_swarm=swarm, + conditions=[ + condition1, + ], + fn_viscosity=viscosityFn, + fn_bodyforce=buoyancyFn, +) + +solver = uw.systems.Solver(stokes) + +penalty = 1e6 +solver.set_penalty(penalty) + +#solver.set_inner_method("lu") +#solver.set_inner_method("superlu") +solver.set_inner_method("mumps") +#solver.set_inner_method("superludist") +#solver.set_inner_method("mg") +#solver.set_inner_method("nomg") + +# solver.set_penalty(1.0e10) # higher penalty = larger stability +# solver.options.scr.ksp_rtol = 1.0e-3 + +# nl_tol = 2.e1 +#nl_tol = 5.e-3 + +surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=top) +surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=top) + +def calibrate_pressure(): + + global pressureField + global surfaceArea + global surfacePressureIntegral + + (area,) = surfaceArea.evaluate() + (p0,) = surfacePressureIntegral.evaluate() + pressureField.data[:] -= p0 / area + + print (f'Calibration pressure {p0 / area}') + +# test it out +try: + # nl_tol = 1e-2 + # nl_tol = 5.e-3 + # solver.solve(nonLinearIterate=True, nonLinearTolerance=nl_tol, callback_post_solve=calibrate_pressure) + solver.solve(nonLinearIterate=True, callback_post_solve=calibrate_pressure) + solver.print_stats() +except: + print("Solver died early..") + exit(0) + + +# ## Output + +# In[8]: + + +## correct the pressure +meshCorrectedPressure = mesh.add_variable( 1 ) +meshSecondCorrectedPressure = mesh.add_variable( 1 ) + +## a) from the pressureField +meshCorrectedPress = uw.utils.MeshVariable_Projection( meshCorrectedPressure, pressureField, type=1 ) +meshCorrectedPress.solve() + +## b) from the stranirate tensor +pressureFn = (strainRateTensor[0] + strainRateTensor[1]) * viscosityFn +meshSecondCorrectedPress = uw.utils.MeshVariable_Projection( meshSecondCorrectedPressure, pressureFn, type=1 ) +meshSecondCorrectedPress.solve() + +## comment: +## note that the two integrals a) and b) above result in exactly the same pressure (as they should) + + +# In[9]: + + +## correct the shear stress +devStressFn = 2.0 * viscosityFn * strainRateTensor + +meshDevStress = mesh.add_variable( 1 ) + +projectorStress = uw.utils.MeshVariable_Projection( meshDevStress, fn.tensor.second_invariant(devStressFn), type=0 ) +projectorStress.solve() + +## maybe we can project the values twice ? +#projectorStress = uw.utils.MeshVariable_Projection( meshDevStress, meshDevStress, type=0 ) +#projectorStress.solve() + + +# In[20]: + + +# save to disc + +outputFile = os.path.join(os.path.abspath("."), outputPath + "output_" + str(maxX) + ".csv") + +with open(outputFile, "w") as text_file: + + text_file.write("X," + "Y," + "surf vx," + "surf vy," + "basal vx," + "tau integr.," + "tau dir.," + "P integr.," + "P dir.," + "\n") + + for i, j, k in zip(iceRockInterfaceSet, iceAirInterfaceSet, bottomInterfaceSet): + + textline = str(mesh.data[i][0]) + "," + str(mesh.data[i][1] ) + "," + str(velocityField.data[j][0]) + "," + str(velocityField.data[j][1]) + "," + str(velocityField.data[i][0]) + "," + str(meshDevStress.data[k][0]) + "," + str(shearStressFn.evaluate((mesh.data[k][0],mesh.data[k][1]))[0][0]) + "," + str(meshCorrectedPressure.data[k][0]) + "," + str(pressureFn.evaluate((mesh.data[k][0], mesh.data[k][1]))[0][0]) + "\n" + + text_file.write(textline) + + +# In[21]: + + +# plot saved files + +# plot figures + +figinflow = vis.Figure(figsize=(1800,500), title="free slip with in/out flow") +figinflow.append(vis.objects.VectorArrows(mesh, velocityField)) +figinflow.append(vis.objects.Surface(mesh, uw.function.math.dot(velocityField,velocityField), colours="gebco")) +figinflow.save_image(outputPath + "velocity_" + str(maxX) + ".png") + +figMaterial = vis.Figure(figsize=(1800, 500), title="Material") +figMaterial.append(vis.objects.Points( swarm, materialVariable, pointSize=1.0)) +figMaterial.save_image(outputPath + "material_" + str(maxX) + ".png") + +figDensity = vis.Figure(figsize=(1800, 500), title="Density") +figDensity.append(vis.objects.Points( swarm, particleDensity, pointSize=1.0)) +figDensity.save_image(outputPath + "density_" + str(maxX) + ".png") + +figViscosity = vis.Figure(figsize=(1800, 500), title="viscosity") +figViscosity.append(vis.objects.Surface(mesh, logViscosityFn)) +figViscosity.save_image(outputPath + "logviscosity_" + str(maxX) + ".png") + +figPressure = vis.Figure(figsize=(1800, 500), title="pressure") +figPressure.append(vis.objects.Surface(mesh, pressureField)) +figPressure.save_image(outputPath + "pressure_" + str(maxX) + ".png") + + +# In[ ]: + + +# finally save meshvars, swarmvars, xdmf vars +xdmf_info_mesh = mesh.save('mesh.h5') +xdmf_info_meshVelocityField = velocityField.save('meshVelocityField.h5') +xdmf_info_meshDevStress = meshDevStress.save('meshDevStress.h5') +xdmf_info_meshCorrectedPressure = meshCorrectedPressure.save('meshCorrectedPressure.h5') + +# swarm +xdmf_info_swarm = swarm.save('swarm.h5') +xdmf_info_swarmMaterialVariable = materialVariable.save('swarmMaterialVariable.h5') + +# xdmf mesh +velocityField.xdmf('meshVelocityField.xdmf', xdmf_info_meshVelocityField, "velocityField", xdmf_info_mesh, "TheMesh", modeltime=0.0) +meshDevStress.xdmf('meshDevStress.xdmf', xdmf_info_meshDevStress, "devStressField", xdmf_info_mesh, "TheMesh", modeltime=0.0) +meshCorrectedPressure.xdmf('meshCorrectedPressure.xdmf', xdmf_info_meshCorrectedPressure, "correctedPressureField", xdmf_info_mesh, "TheMesh", modeltime=0.0) + +# xdmf swarm +materialVariable.xdmf('swarmMaterialVariable.xdmf', xdmf_info_swarmMaterialVariable, "material", xdmf_info_swarm, "TheSwarm", modeltime=0.0) + + +# In[ ]: + + + + diff --git a/model_code_inputs/Exp_E-no-slip-version.py b/model_code_inputs/Exp_E-no-slip-version.py new file mode 100644 index 0000000..c42aa4b --- /dev/null +++ b/model_code_inputs/Exp_E-no-slip-version.py @@ -0,0 +1,413 @@ +# --- +# jupyter: +# jupytext: +# formats: ipynb,md,py:light +# text_representation: +# extension: .py +# format_name: light +# format_version: '1.5' +# jupytext_version: 1.13.5 +# kernelspec: +# display_name: Python 3 (ipykernel) +# language: python +# name: python3 +# --- + +# This model of Exp E is from Feb 2022. +# +# This is the 'free slip' version, as described by Pattyn 2008. +# +# **Important note:** there is still no-slip for most of the model area! Only the section where 2200 <= x <= 2500 is free-slip! +# +# Due to the irregular and mostly oblque basal topography we can not simply use the common free-slip condition - which would have to enable slip in x _and_ y. This can not work, obviously. +# +# Idea: have a basal layer with a viscosity of 0. +# +# It models the glacier described in Pattyn (...) as a deformed mesh. Some ingenuity is necessary for this to work, so maybe there will be another version necessary. Obe that just uses particles. + +# # Basic python imports and model settings + +# + +from underworld import function as fn +import underworld as uw + +import underworld.visualisation as vis + +import matplotlib.pyplot as pyplot +import numpy as np +from scipy.spatial import distance + +import math +import os +import sys + +import time + +from scipy.signal import savgol_filter + +g = 9.81 +ice_density = 910. + +A = 1e-16 +n = 3. +# - + +# ## Get topo info from file + +# + +topo = np.genfromtxt("topo.csv") +topo_base = topo[:, 0:-2] +topo_surf = topo[:, 0:-1] +topo_surf = np.delete(topo_surf, obj=1, axis=1) + +pyplot.plot(topo_base[:,0], topo_base[:,-1]) +pyplot.plot(topo_surf[:,0], topo_surf[:,-1]) + +pyplot.show() + +# + +resX = topo_base.shape[0] - 1 +resY = topo_base.shape[0] - 1 + 1 # the trailing +1 because we need a higher resolution compared with the no-slip experiments + +air_height = 50. + +DeltaY = np.max(topo_surf[:,1]) + air_height - np.min(topo_base[:,1]) + +maxX = np.max(topo_surf[:,0]) +maxY = np.max(topo_surf[:,1]) + air_height + +minX = np.min(topo_base[:,0]) +minY = np.min(topo_base[:,1]) - DeltaY / (resY - 1) + +print(f"resX: {resX}, resY: {resY}" ) +print(f"minX: {minX}, minY: {minY}" ) +print(f"maxX: {maxX}, maxY: {maxY}" ) + +cell_height = maxY / resY +cell_width = maxX / resX +# - + +# # The mesh + +# + +elementType = "Q1/dQ0" + +mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType), + elementRes=(resX, resY), + minCoord=(minX, minY), + maxCoord=(maxX, maxY), + periodic=[False, False]) + +submesh = mesh.subMesh + +velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +pressureField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +pressureField.data[:] = 0. +velocityField.data[:] = [0., 0.] +# - + +# ## Deform the mesh + +figMesh = vis.Figure(figsize=(1200,600)) +figMesh.append( vis.objects.Mesh(mesh, nodeNumbers=False)) +figMesh.show() + +# + +dx = (maxX - minX) / resX +dy = (maxY - minY) / resY + +def mesh_deform_base_Ind(section, fixPoint_index, fixPoint, mi): + + section[fixPoint_index] = fixPoint + seqN = len(section) + + for index in range(len(section)): + + maxCoord = np.max(section) + minCoord = np.min(section) + + section[index] = fixPoint + (index-fixPoint_index)*(maxCoord-fixPoint) / (seqN-fixPoint_index-1) + zz_pow = (section[index] - fixPoint)**mi + zz_pow_max = (maxCoord - fixPoint)**mi + section[index] =fixPoint + (section[index]-fixPoint) * zz_pow / zz_pow_max + + return (section) + +with mesh.deform_mesh(): + + for indexx in range(resX + 1): + + start_x = dx * indexx + + interface_y = topo_base[indexx, 1] + + ind = np.where( abs(mesh.data[:, 0] - start_x) < 0.01*dx ) + mesh.data[ind[0][1:],1] = mesh_deform_base_Ind(mesh.data[ind[0][1:], 1], 0, interface_y, 0.2) + mesh.data[ind[0][0],1] = interface_y - dy + +# - + +figMesh.show() + +# # A material swarm + +# + +# Initialise the 'materialVariable' data to represent different materials. +materialV = 0 # ice, isotropic +materialA = 1 # air +materialS = 2 # soft ('0'-viscosity) material +materialH = 3 # hard ('inf'-viscosity) material + +part_per_cell = 50 + +swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) +swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm, particlesPerCell=part_per_cell) +swarm.populate_using_layout(layout=swarmLayout) + +materialVariable = swarm.add_variable(dataType="int", count=1) + +coord = fn.input() + +materialVariable.data[:] = materialA + +iceBody = fn.shape.Polygon( np.append(topo_surf, topo_base[::-1], axis=0) ) +slipperyBody = fn.shape.Polygon( np.append(topo_base, topo_base[::-1] - (0, 50), axis=0) ) + +for index in range( len(swarm.particleCoordinates.data) ): + + co = swarm.particleCoordinates.data[index][:] + + if iceBody.evaluate (tuple (co)): + materialVariable.data[index] = materialV + elif slipperyBody.evaluate(tuple (co)): + if 2200 <= co[0] <= 2500: + materialVariable.data[index] = materialS + else: + materialVariable.data[index] = materialH + +measurementSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# create pop control object +pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell) +advector1 = uw.systems.SwarmAdvector(swarm=swarm, velocityField=velocityField, order=2) + +pop_control2 = uw.swarm.PopulationControl(measurementSwarm) +advector2 = uw.systems.SwarmAdvector(swarm=measurementSwarm, velocityField=velocityField, order=2) +# - + +figMaterials = vis.Figure(figsize=(1200,600)) +figMaterials.append(vis.objects.Points(swarm, materialVariable, pointSize=1.0, rulers=True)) +figMaterials.show() + +# # Boundary conditions + +# + +sideWalls = mesh.specialSets["MaxJ_VertexSet"] + mesh.specialSets["MinJ_VertexSet"] +vertWalls = mesh.specialSets["MaxI_VertexSet"] + mesh.specialSets["MinI_VertexSet"] + +botWall = mesh.specialSets["MinJ_VertexSet"] +surfWalls = sideWalls = mesh.specialSets["MaxJ_VertexSet"] + +# Dirichlet +condition = uw.conditions.DirichletCondition(variable = velocityField, indexSetsPerDof=(botWall, botWall)) + +velocityField.data[:] = [0., 0.] +# - + +strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient) +strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor) + +# # Viscosity, density, buoyancy + +# + +minViscosityIceFn = fn.misc.constant(1e+6 / 3.1536e7) +maxViscosityIceFn = fn.misc.constant(1e+15 / 3.1536e7) + +viscosityFnAir = fn.misc.constant(1e9 / 3.1536e7) + +# viscosity of the hard (NoSlip) basal layer +viscosityFnNS = fn.misc.constant(1e23 / 3.1536e7) + +# viscosity of the soft basal layer +viscosityFnS = fn.misc.constant(8e8 / 3.1536e7) + +viscosityFnIceBase = 0.5 * A ** (-1./n) * (strainRate_2ndInvariantFn**((1.-n) / float(n))) +viscosityFnIce = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn) + +viscosityMap = { + materialV: viscosityFnIce, + materialA: viscosityFnAir, + materialH: viscosityFnNS, + materialS: viscosityFnS, + } + +viscosityFn = fn.branching.map( fn_key=materialVariable, mapping=viscosityMap ) + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +densityFnAir = fn.misc.constant( 0.001 ) +densityFnIce = fn.misc.constant( ice_density ) + +densityMap = { + materialA: densityFnAir, + materialV: densityFnIce, + materialH: densityFnIce, + materialS: densityFnIce, + } + +densityFn = fn.branching.map(fn_key=materialVariable, mapping=densityMap) + +buoyancyFn = densityFn * (0., -1.) * 9.81 +# - + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +# # Solver + +# + +stokes = uw.systems.Stokes( + velocityField=velocityField, + pressureField=pressureField, + voronoi_swarm=swarm, + conditions=condition, + fn_viscosity=viscosityFn, + fn_bodyforce=buoyancyFn, +) + +solver = uw.systems.Solver(stokes) + +solver.set_inner_method("mumps") + +surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=surfWalls) +surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=surfWalls) + +def calibrate_pressure(): + + global pressureField + global surfaceArea + global surfacePressureIntegral + + (area,) = surfaceArea.evaluate() + (p0,) = surfacePressureIntegral.evaluate() + pressureField.data[:] -= p0 / area + + print (f'Calibration pressure {p0 / area}') + +# test it out +try: + exec_time = time.time() + solver.solve(nonLinearIterate=True, callback_post_solve=calibrate_pressure) + exec_time = time.time() - exec_time + + # print full stats to a file + solver.print_stats() +except: + print("Solver died early..") + exit(0) + +print (f'Solving took: {exec_time} seconds') +# - + +figVel = vis.Figure(figsize=(1200,600)) +figVel.append(vis.objects.Surface(mesh, fn.math.sqrt(fn.math.dot(velocityField, velocityField)), colourBar=True ))#fn_mask = materialVariable)) +figVel.show() + +# # Output + +# + +#### Filename +outputFile = os.path.join(os.path.abspath("."), "jla"+"1e001"+ ".csv") +print(outputFile) + +#### Smooth the stress +meshStressTensor = uw.mesh.MeshVariable(mesh, 3) +projectorStress = uw.utils.MeshVariable_Projection( meshStressTensor, devStressFn, type=0 ) +projectorStress.solve() + +#### Smooth the velocity +meshVelocity = uw.mesh.MeshVariable(mesh, 2) +projectorV = uw.utils.MeshVariable_Projection( meshVelocity, velocityField, type=0 ) +projectorV.solve() + +#### Smooth the pressure +meshP = uw.mesh.MeshVariable(mesh, 1) +projectorP = uw.utils.MeshVariable_Projection( meshP, pressureField, type=0 ) +projectorP.solve() + +#### Points +sub = 0. #cell_height +add = cell_height + +surf_pos = topo_surf +base_pos = topo_base + +#### Get the surface velocity +vxs = meshVelocity.evaluate(surf_pos).transpose()[0] +vys = meshVelocity.evaluate(surf_pos).transpose()[1] + +vtots = np.sqrt( vxs*vxs + vys*vys ) + +#### Get the basal velocity +vxb = meshVelocity.evaluate(base_pos).transpose()[0] +vyb = meshVelocity.evaluate(base_pos).transpose()[1] + +vtotb = np.sqrt( vxb*vxb + vyb*vyb ) + +#### Get the pressure +P = meshP.evaluate(base_pos).squeeze() +#P = pressureField.evaluate(base_pos).squeeze() + +#### Get the shearstress +sxy = meshStressTensor.evaluate(base_pos).squeeze()[:,2] +#sxy = devStressFn.evaluate(base_pos).squeeze()[:,2] + +#### plot pressure from grid / theoretical / difference +print("DeltaP") +#pyplot.plot((maxY - base_ypos[:]) * 9.81 * 910, color='red') +smoothed_2dg = savgol_filter(P, window_length = 3, polyorder = 2) +#pyplot.plot(P[ind], color='blue') +#pyplot.plot(P - (maxY - base_pos[ind, 1].squeeze()) * 9.81 * 910., color='green') +pyplot.plot(smoothed_2dg, color='black') +pyplot.show() + +#### plot vx at surface +print("vxs") +smoothed_2dg = savgol_filter(vtots, window_length = 3, polyorder = 2) +#pyplot.plot(vxs[ind], color='red') +pyplot.plot(smoothed_2dg, color='black') +pyplot.show() + +### plot shear stress +print("Shear stress") +smoothed_2dg = savgol_filter(sxy / 1000, window_length = 3, polyorder = 2) +#pyplot.plot (sxz[ind] / 1000., color='red') +pyplot.plot (smoothed_2dg, color='black') +pyplot.show () + +#### output to file +with open(outputFile, "w") as text_file: + + for i in range(0, resX+1): + + # Ausgabe [x] [y] + textline = str("{:.7f}".format(surf_pos[i, 0] / maxX)) + "\t" + + #Ausgabe Geschwindigkeiten Surface[vx] [vy] [vz] + textline += str("{:.7f}".format(vtots[i])) + "\t" + str("{:.7f}".format(vys[i])) + "\t" + + #Ausgabe Geschwindigkeiten Basis [vx] [vy] + #textline += str("{:.7f}".format(vxb[i])) + "\t" + + # Scherspannung Basis Tensoren [Txz] [Tyz] + textline += str("{:.7f}".format(sxy[i] / 1000.)) + "\t" + + # Ausgabe delta p + textline += str("{:.7f}".format( (P[i] - float((surf_pos[i, 1] - base_pos[i, 1]) * 9.81 * 910 )) / 1000)) + "\n" + + text_file.write(textline) +# - + + diff --git a/model_code_inputs/Exp_E_mixed-slip-version.py b/model_code_inputs/Exp_E_mixed-slip-version.py new file mode 100644 index 0000000..c099647 --- /dev/null +++ b/model_code_inputs/Exp_E_mixed-slip-version.py @@ -0,0 +1,384 @@ +# --- +# jupyter: +# jupytext: +# formats: ipynb,md,py:light +# text_representation: +# extension: .py +# format_name: light +# format_version: '1.5' +# jupytext_version: 1.13.5 +# kernelspec: +# display_name: Python 3 (ipykernel) +# language: python +# name: python3 +# --- + +# This model of Exp E is from Feb 2022. +# +# It models the glacier described in Pattyn (...) as a deformed mesh. Some ingenuity is necessary for this to work, so maybe there will be another version necessary. Obe that just uses particles. + +# # Basic python imports and model settings + +# + +from underworld import function as fn +import underworld as uw + +import underworld.visualisation as vis + +import matplotlib.pyplot as pyplot +import numpy as np +from scipy.spatial import distance + +import math +import os +import sys + +import time + +from scipy.signal import savgol_filter + +g = 9.81 +ice_density = 910. + +A = 1e-16 +n = 3. +# - + +# ## Get topo info from file + +# + +topo = np.genfromtxt("topo.csv") +topo_base = topo[:, 0:-2] +topo_surf = topo[:, 0:-1] +topo_surf = np.delete(topo_surf, obj=1, axis=1) + +pyplot.plot(topo_base[:,0], topo_base[:,-1]) +pyplot.plot(topo_surf[:,0], topo_surf[:,-1]) + +pyplot.show() + +# + +resX = topo_base.shape[0] - 1 +resY = topo_base.shape[0] - 1 + +air_height = 50. + +maxX = np.max(topo_surf[:,0]) +maxY = np.max(topo_surf[:,1]) + air_height + +minX = np.min(topo_base[:,0]) +minY = np.min(topo_base[:,1]) + +print(f"resX: {resX}, resY: {resY}" ) +print(f"minX: {minX}, minY: {minY}" ) +print(f"maxX: {maxX}, maxY: {maxY}" ) + +cell_height = maxY / resY +cell_width = maxX / resX +# - + +# # The mesh + +# + +elementType = "Q1/dQ0" + +mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType), + elementRes=(resX, resY), + minCoord=(minX, minY), + maxCoord=(maxX, maxY), + periodic=[False, False]) + +submesh = mesh.subMesh + +velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +pressureField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +pressureField.data[:] = 0. +velocityField.data[:] = [0., 0.] +# - + +# ## Deform the mesh + +figMesh = vis.Figure(figsize=(1200,600)) +figMesh.append( vis.objects.Mesh(mesh, nodeNumbers=True)) + +# + +dx = (maxX - minX) / resX +dy = (maxX - maxY) / resY + +def mesh_deform_base_Ind(section, fixPoint_index, fixPoint, mi): + + section[fixPoint_index] = fixPoint + seqN = len(section) + + for index in range(len(section)): + + maxCoord = np.max(section) + minCoord = np.min(section) + + section[index] = fixPoint + (index-fixPoint_index)*(maxCoord-fixPoint) / (seqN-fixPoint_index-1) + zz_pow = (section[index] - fixPoint)**mi + zz_pow_max = (maxCoord - fixPoint)**mi + section[index] =fixPoint + (section[index]-fixPoint) * zz_pow / zz_pow_max + + return (section) + +with mesh.deform_mesh(): + + for indexx in range(resX + 1): + + start_x = dx * indexx + + interface_y = topo_base[indexx, 1] + + ind = np.where( abs(mesh.data[:, 0] - start_x) < 0.01*dx ) + + mesh.data[ind[0],1] = mesh_deform_base_Ind(mesh.data[ind[0], 1], 0, interface_y, 0.2) + +# - + +figMesh.show() + +# # A material swarm + +# + +# Initialise the 'materialVariable' data to represent different materials. +materialV = 0 # ice, isotropic +materialA = 1 # air + +part_per_cell = 50 + +swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) +swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm, particlesPerCell=part_per_cell) +swarm.populate_using_layout(layout=swarmLayout) + +materialVariable = swarm.add_variable(dataType="int", count=1) + +coord = fn.input() + +materialVariable.data[:] = materialA + +iceBody = fn.shape.Polygon( np.append(topo_surf, topo_base[::-1], axis=0) ) + +for index in range( len(swarm.particleCoordinates.data) ): + + co = swarm.particleCoordinates.data[index][:] + + if iceBody.evaluate (tuple (co)): + materialVariable.data[index] = materialV + +measurementSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +# create pop control object +pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell) +advector1 = uw.systems.SwarmAdvector(swarm=swarm, velocityField=velocityField, order=2) + +pop_control2 = uw.swarm.PopulationControl(measurementSwarm) +advector2 = uw.systems.SwarmAdvector(swarm=measurementSwarm, velocityField=velocityField, order=2) +# - + +figMaterials = vis.Figure(figsize=(1200,600)) +figMaterials.append(vis.objects.Points(swarm, materialVariable, pointSize=1.0, rulers=True)) +figMaterials.show() + +# # Boundary conditions + +# + +sideWalls = mesh.specialSets["MaxJ_VertexSet"] + mesh.specialSets["MinJ_VertexSet"] +vertWalls = mesh.specialSets["MaxI_VertexSet"] + mesh.specialSets["MinI_VertexSet"] + +botWall = mesh.specialSets["MinJ_VertexSet"] +surfWalls = sideWalls = mesh.specialSets["MaxJ_VertexSet"] + +# Dirichlet +condition = uw.conditions.DirichletCondition(variable = velocityField, indexSetsPerDof=(botWall, botWall)) + +velocityField.data[:] = [0., 0.] +# - + +strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient) +strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor) + +# # Viscosity, density, buoyancy + +# + +minViscosityIceFn = fn.misc.constant(1e+6 / 3.1536e7) +maxViscosityIceFn = fn.misc.constant(1e+15 / 3.1536e7) + +viscosityFnAir = fn.misc.constant(1e9 / 3.1536e7) + +viscosityFnIceBase = 0.5 * A ** (-1./n) * (strainRate_2ndInvariantFn**((1.-n) / float(n))) +viscosityFnIce = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn) + +viscosityMap = { + materialV: viscosityFnIce, + materialA: viscosityFnAir, + } + +viscosityFn = fn.branching.map( fn_key=materialVariable, mapping=viscosityMap ) + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +densityFnAir = fn.misc.constant( 0.001 ) +densityFnIce = fn.misc.constant( ice_density ) + +densityMap = { + materialA: densityFnAir, + materialV: densityFnIce, + } + +densityFn = fn.branching.map(fn_key=materialVariable, mapping=densityMap) + +buoyancyFn = densityFn * (0., -1.) * 9.81 +# - + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +# # Solver + +# + +stokes = uw.systems.Stokes( + velocityField=velocityField, + pressureField=pressureField, + voronoi_swarm=swarm, + conditions=condition, + fn_viscosity=viscosityFn, + fn_bodyforce=buoyancyFn, +) + +solver = uw.systems.Solver(stokes) + +solver.set_inner_method("mumps") + +surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=surfWalls) +surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=surfWalls) + +def calibrate_pressure(): + + global pressureField + global surfaceArea + global surfacePressureIntegral + + (area,) = surfaceArea.evaluate() + (p0,) = surfacePressureIntegral.evaluate() + pressureField.data[:] -= p0 / area + + print (f'Calibration pressure {p0 / area}') + +# test it out +try: + exec_time = time.time() + solver.solve(nonLinearIterate=True, callback_post_solve=calibrate_pressure) + exec_time = time.time() - exec_time + + # print full stats to a file + solver.print_stats() +except: + print("Solver died early..") + exit(0) + +print (f'Solving took: {exec_time} seconds') +# - + +figVel = vis.Figure(figsize=(1200,600)) +figVel.append(vis.objects.Surface(mesh, fn.math.dot(velocityField, velocityField), colourBar=True ))#fn_mask = materialVariable)) +figVel.show() + +# # Output + +# + +#### Filename +outputFile = os.path.join(os.path.abspath("."), "jla"+"1e000"+ ".csv") +print(outputFile) + +#### Smooth the stress +meshStressTensor = uw.mesh.MeshVariable(mesh, 3) +projectorStress = uw.utils.MeshVariable_Projection( meshStressTensor, devStressFn, type=0 ) +projectorStress.solve() + +#### Smooth the velocity +meshVelocity = uw.mesh.MeshVariable(mesh, 2) +projectorV = uw.utils.MeshVariable_Projection( meshVelocity, velocityField, type=0 ) +projectorV.solve() + +#### Smooth the pressure +meshP = uw.mesh.MeshVariable(mesh, 1) +projectorP = uw.utils.MeshVariable_Projection( meshP, pressureField, type=0 ) +projectorP.solve() + +#### Points +sub = cell_height +add = cell_height + +surf_pos = topo_surf +base_pos = topo_base + +#### Get the surface velocity +vxs = meshVelocity.evaluate(surf_pos).transpose()[0] +vys = meshVelocity.evaluate(surf_pos).transpose()[1] + +vtots = np.sqrt( vxs*vxs + vys*vys ) + +#### Get the basal velocity +vxb = meshVelocity.evaluate(base_pos).transpose()[0] +vyb = meshVelocity.evaluate(base_pos).transpose()[1] + +vtotb = np.sqrt( vxb*vxb + vyb*vyb ) + +#### Get the pressure +P = meshP.evaluate(base_pos).squeeze() +#P = pressureField.evaluate(base_pos).squeeze() + +#### Get the shearstress +sxy = meshStressTensor.evaluate(base_pos).squeeze()[:,2] +#sxy = devStressFn.evaluate(base_pos).squeeze()[:,2] + +#### plot pressure from grid / theoretical / difference +print("DeltaP") +#pyplot.plot((maxY - base_ypos[:]) * 9.81 * 910, color='red') +smoothed_2dg = savgol_filter(P, window_length = 3, polyorder = 2) +#pyplot.plot(P[ind], color='blue') +#pyplot.plot(P - (maxY - base_pos[ind, 1].squeeze()) * 9.81 * 910., color='green') +pyplot.plot(smoothed_2dg, color='black') +pyplot.show() + +#### plot vx at surface +print("vxs") +smoothed_2dg = savgol_filter(vtots, window_length = 3, polyorder = 2) +#pyplot.plot(vxs[ind], color='red') +pyplot.plot(smoothed_2dg, color='black') +pyplot.show() + +### plot shear stress +print("Shear stress") +smoothed_2dg = savgol_filter(sxy / 1000, window_length = 3, polyorder = 2) +#pyplot.plot (sxz[ind] / 1000., color='red') +pyplot.plot (smoothed_2dg, color='black') +pyplot.show () + +#### output to file +with open(outputFile, "w") as text_file: + + for i in range(0, resX+1): + + # Ausgabe [x] [y] + textline = str("{:.7f}".format(surf_pos[i, 0] / maxX)) + "\t" + + #Ausgabe Geschwindigkeiten Surface[vx] [vy] [vz] + textline += str("{:.7f}".format(vtots[i])) + "\t" + str("{:.7f}".format(vys[i])) + "\t" + + #Ausgabe Geschwindigkeiten Basis [vx] [vy] + #textline += str("{:.7f}".format(vxb[i])) + "\t" + + # Scherspannung Basis Tensoren [Txz] [Tyz] + textline += str("{:.7f}".format(sxy[i] / 1000.)) + "\t" + + # Ausgabe delta p + textline += str("{:.7f}".format( (P[i] - float((surf_pos[i, 1] - base_pos[i, 1]) * 9.81 * 910 )) / 1000)) + "\n" + + text_file.write(textline) +# - + + diff --git a/model_code_inputs/Exp_F-3D.py b/model_code_inputs/Exp_F-3D.py new file mode 100644 index 0000000..66f0dd8 --- /dev/null +++ b/model_code_inputs/Exp_F-3D.py @@ -0,0 +1,493 @@ +#!/usr/bin/env python +# coding: utf-8 + +# # Basic python imports and model settings + +# In[ ]: + + +# import underworld.visualisation as vis + +from underworld import function as fn +import underworld as uw +import numpy as np + +from mpi4py import MPI + +comm = MPI.COMM_WORLD +rank = comm.Get_rank() +size = comm.Get_size() + +import math +import os +import sys + +import time + +LoadFromFile = False + +resX = 240 +resY = 48 +resZ = 240 + +#resX = 128 +#resY = 16 +#resZ = 128 + +#resX = 28 +#resY = 5 +#resZ = 28 + +H0 = 1000. # surface height (snow) +sigma = 10. * H0 # width gaussian bump 10.*H0 +a0 = 100. # amplitude gaussian bump +alpha = 3. * np.pi / 180. # dip of surface + +minX, maxX = -(100. * H0) / 2., (100. * H0) / 2. +#minX, maxX = -(20. * H0) / 2., (20. * H0) / 2. +minY, maxY = 0., 1100. +minZ, maxZ = -(100. * H0) / 2., (100. * H0) / 2. + +g = 9.81 +ice_density = 910. + +A = 2.140373e-7 +n = 1. + +print (f'Hello from process {rank} out of {size}') + +# generate output path +outputPath = os.path.join(os.path.abspath("."), "PeriZPICoutput_" + str(maxY)+ "_res_" + str(resX) + "_x_" + str(resY) + "_x_" + str(resZ) + "/") +inputPath = outputPath + +if rank == 0: + if not os.path.exists(outputPath): + os.makedirs(outputPath) +# os.chdir(outputPath) +comm.Barrier() + +print (f'Hello from process {rank} out of {size}') + +cell_height = maxY / resY +cell_width = maxX / resX +cell_depth = maxZ / resZ + +coord = fn.input() + +if(LoadFromFile == True): + step = 220 + step_out = 10 + nsteps = 10000 + timestep = float(np.load(outputPath+"time"+str(step).zfill(4)+".npy")) + +else: + step = 0 + step_out = 20 + nsteps = 10000 + timestep = 0. + + +elementType = "Q1/dQ0" + +mesh = uw.mesh.FeMesh_Cartesian(elementType=(elementType), + elementRes=(resX, resY, resZ), + minCoord=(minX, minY, minZ), + maxCoord=(maxX, maxY, maxZ), + periodic=[True, False, True]) + +def mesh_deform(section,fixPoint,mi,case): + # fixPoint: the position to be refined + # mi: representing the gradient of mesh resolution; the larger mi, the larger gradient + if case == 0: + maxCoord = maxX + minCoord = minX + elif case ==1: + maxCoord = maxY + minCoord = minY + else: + maxCoord = maxZ + minCoord = minZ + + for index in range(len(section)): + + if section[index]<=fixPoint: + zz_sqrt = (fixPoint-section[index])**mi + zz_sqrt_max = (fixPoint-minCoord)**mi + section[index] = fixPoint-(fixPoint-section[index])*zz_sqrt/zz_sqrt_max + + if section[index]>=fixPoint: + zz_sqrt = (section[index]-fixPoint)**mi + zz_sqrt_max = (maxCoord-fixPoint)**mi + section[index] =fixPoint+(section[index]-fixPoint)*zz_sqrt/zz_sqrt_max + + return section + +def mesh_deform_Ind(section,Point0,fixPoint,mi,case): + section_copy = np.copy(section) +# section[fixPoint_index] = fixPoint + + if case == 0: + maxCoord = maxX + minCoord = minX + elif case ==1: + maxCoord = maxY + minCoord = minY + else: + maxCoord = maxZ + minCoord = minZ + + + # fixPoint: the position to be refined + # mi: representing the gradient of mesh resolution; the larger mi, the larger gradient + for index in range(len(section)): + + if section_copy[index] >= Point0: + + section[index] = fixPoint + (maxCoord-fixPoint)*((section_copy[index]-Point0)/(maxCoord-Point0))**mi + + return section + + +mesh.reset() + +dx = (maxX-minX)/resX +dy = (maxZ-minZ)/resZ + +with mesh.deform_mesh(): + for index_j in range(resZ+1): + for index in range(resX+1): + start_x = minX+dx*index + start_y = minZ+index_j*dy + interface_z = a0 * np.exp( -(start_x**2. + start_y**2.) / sigma**2.) + + indx = np.where(abs(mesh.data[:,0]-start_x)<0.01*dx) + indy = np.where(abs(mesh.data[:,2]-start_y)<0.01*dx) + ind = np.intersect1d(indx[0],indy[0]) + + mesh.data[ind,1] = mesh_deform_Ind(mesh.data[ind,1],0.,interface_z,1.0,1) + +with mesh.deform_mesh(): + + mesh.data[:,0] = mesh_deform(mesh.data[:,0],0.,0.2,0) + mesh.data[:,2] = mesh_deform(mesh.data[:,2],0.,0.2,2) + + +velocityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +pressureField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +previousVmMesh = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +velAMesh = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) +vel_effMesh = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=mesh.dim) + +viscosityField = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=1) + +strainRateField = mesh.add_variable(nodeDofCount=1) + +pressureField.data[:] = 0. +velocityField.data[:] = [0., 0., 0.] + + + +# # The swarm + +part_per_cell = 125 +swarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) + +previousVm = swarm.add_variable( dataType="double", count=3 ) +velA = swarm.add_variable( dataType="double", count=3 ) +vel_eff = swarm.add_variable( dataType="double", count=3 ) + +# Initialise the 'materialVariable' data to represent different materials. +materialV = 1 # ice +materialA = 2 # Air + +if(LoadFromFile == False): + swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm, particlesPerCell=part_per_cell) + #swarmLayout = uw.swarm.layouts.PerCellGaussLayout( swarm=swarm, gaussPointCount=5 ) + swarm.populate_using_layout(layout=swarmLayout) + +# create pop control object +pop_control1 = uw.swarm.PopulationControl(swarm, aggressive=True, particlesPerCell=part_per_cell) + +# ### Create a particle advection system +# Note that we need to set up one advector systems for each particle swarm (our global swarm and a separate one if we add passive tracers). +advector1 = uw.systems.SwarmAdvector(swarm=swarm, velocityField=velocityField, order=2) + + + +# ## Surfaceswarm in order to measure the change in surface height + +# In[ ]: + + +## swarms to track the deformation +surfaceSwarm = uw.swarm.Swarm(mesh=mesh, particleEscape=True) +previousVmB = surfaceSwarm.add_variable( dataType="double", count=3 ) +velB = surfaceSwarm.add_variable( dataType="double", count=3 ) +vel_effB = surfaceSwarm.add_variable( dataType="double", count=3 ) + +# create pop control object +# pop_control3 = uw.swarm.PopulationControl(surfaceSwarm) + +# create wireframe +if(LoadFromFile == False): + p = (int(part_per_cell**0.33333) + 1) * resX + surfacePoints = np.array(np.meshgrid(np.linspace(minX, maxX, p), H0, np.linspace(minZ, maxZ, p))).T.reshape(-1, 3) + surfaceSwarm.add_particles_with_coordinates(surfacePoints) + +# create advector +advector3 = uw.systems.SwarmAdvector(swarm=surfaceSwarm, velocityField=velocityField, order=2) + + + +# Tracking different materials + +materialVariable = swarm.add_variable(dataType="int", count=1) +directorVector = swarm.add_variable( dataType="double", count=3) + +if(LoadFromFile == False): + + coord = fn.input() + # conditions = [ (coord[1] > H0, materialA), + # (coord[1] > fn_basis, materialV), + # (True, materialR)] + conditions = [ (coord[1] > H0, materialA), + (True, materialV)] + + materialVariable.data[:] = fn.branching.conditional(conditions).evaluate(swarm) + + +if(LoadFromFile == True): + surfaceSwarm.load(inputPath+"surfaceSwarm"+str(step).zfill(4)) + swarm.load(inputPath+"swarm"+str(step).zfill(4)) + materialVariable.load(inputPath+"materialVariable"+str(step).zfill(4)) + +# In[ ]: + + +iWalls = mesh.specialSets["MinI_VertexSet"] + mesh.specialSets["MaxI_VertexSet"] +jWalls = mesh.specialSets["MinJ_VertexSet"] + mesh.specialSets["MaxJ_VertexSet"] +kWalls = mesh.specialSets["MinK_VertexSet"] + mesh.specialSets["MaxK_VertexSet"] + +# Surface points +top = mesh.specialSets["MaxJ_VertexSet"] +botSet = mesh.specialSets['MinJ_VertexSet'] + +# Dirichlet +condition = uw.conditions.DirichletCondition(variable = velocityField, indexSetsPerDof=(botSet, botSet, botSet)) + +velocityField.data[:] = [0., 0., 0.] + + +# # Strainrate + +# In[ ]: + + +strainRateTensor = fn.tensor.symmetric(velocityField.fn_gradient) +strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateTensor)+1e-18 + + +# # Effective viscosity, density and gravity + +# In[ ]: + + +viscosityFnRock = fn.misc.constant(1e16 / 31556926) +viscosityFnAir = fn.misc.constant(1e11 / 3.1536e7) + +minViscosityIceFn = fn.misc.constant(1e+11 / 31556926) +maxViscosityIceFn = fn.misc.constant(1e+16 / 31556926) +viscosityFnIceBase = 0.5 * A ** (-1.) #* (strainRate_2ndInvariantFn**((1.-n) / float(n))) +#viscosityFnIce = fn.misc.max(fn.misc.min(viscosityFnIceBase, maxViscosityIceFn), minViscosityIceFn) + +#viscosityFnBase = cell_height * beta_square + +viscosityMap = { + materialV: viscosityFnIceBase, + materialA: 1.*viscosityFnAir, + } + +viscosity2Map = { materialV: 0., + materialA: 0.999*viscosityFnAir } + +viscosityFn = fn.branching.map( fn_key=materialVariable, mapping=viscosityMap ) + + +secondViscosityFn = fn.branching.map( fn_key = materialVariable, + mapping = viscosity2Map ) + +orientation = 0. * math.pi / 180.0 +directorVector.data[:,0] = math.cos(orientation) +directorVector.data[:,1] = math.sin(orientation) +directorVector.data[:,2] = math.sin(orientation) + + +densityFnIce = fn.misc.constant( ice_density ) +densityFnRock = fn.misc.constant( 2700. ) +densityFnAir = fn.misc.constant (0.) + +densityMap = { + materialV: densityFnIce, + materialA: densityFnAir, + } + +densityFn = fn.branching.map( fn_key=materialVariable, mapping=densityMap ) + +surf_inclination = alpha +z_hat = (math.sin(surf_inclination), - math.cos(surf_inclination), 0.) + +buoyancyFn = densityFn * z_hat * 9.81 + + +# In[ ]: + + + +# In[ ]: + + +devStressFn = 2.0 * viscosityFn * strainRateTensor +shearStressFn = strainRate_2ndInvariantFn * viscosityFn * 2.0 + +stokes = uw.systems.Stokes( + velocityField=velocityField, + pressureField=pressureField, + voronoi_swarm=swarm, + conditions=condition, + fn_viscosity=viscosityFn, + fn_bodyforce=buoyancyFn, + _fn_viscosity2 = secondViscosityFn, + _fn_director = directorVector, +) + +solver = uw.systems.Solver (stokes) + +#solver.set_inner_method ("lu") +#solver.set_inner_method ("superlu") +#solver.set_inner_method ("mumps") +#solver.set_inner_method ("superludist") +solver.set_inner_method ("mg") +#solver.set_inner_method ("nomg") + +#solver.set_penalty (1.0e5) # higher penalty = larger stability + +#solver.options.scr.ksp_rtol = 1.0e-3 +#solver.set_penalty( 1.e6 ) +#nl_tol = 1.e-2 # standard value + +surfaceArea = uw.utils.Integral( fn=1.0, mesh=mesh, integrationType='surface', surfaceIndexSet=top) +surfacePressureIntegral = uw.utils.Integral( fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=top) + + +def calibrate_pressure(): + + global pressureField + global surfaceArea + global surfacePressureIntegral + + (area,) = surfaceArea.evaluate() + (p0,) = surfacePressureIntegral.evaluate() + pressureField.data[:] -= p0 / area + + + + +# # Mainloop and flow function + +# In[ ]: +# previousVm.data[:] = 0. +# previousVmB.data[:] = 0. + +def update(): + + + dt = 10*advector1.get_max_dt() + # Advect using this timestep size. + advector1.integrate(dt) # the swarm + # advector2.integrate(dt) # the wireframe swarm + advector3.integrate(dt) # the surface swarm + +# velA.data[:] = velocityField.evaluate(swarm) +# vel_eff.data[:] = 1./2.*(velA.data[:]+1.*previousVm.data[:]) + +# previousVm.data[:] = np.copy(velA.data[:]) + +# with swarm.deform_swarm(): +# swarm.data[:] += vel_eff.data[:]*dt + +# velB.data[:] = velocityField.evaluate(surfaceSwarm) +# vel_effB.data[:] = 1./2.*(velB.data[:]+1.*previousVmB.data[:]) + +# previousVmB.data[:] = np.copy(velB.data[:]) +# with surfaceSwarm.deform_swarm(): +# surfaceSwarm.data[:] += vel_effB.data[:]*dt + +# velAMesh.data[:] = velocityField.evaluate(mesh) +# vel_effMesh.data[:] = 1./2.*(velAMesh.data[:]+1.*previousVmMesh.data[:]) + +# previousVmMesh.data[:] = np.copy(velAMesh.data[:]) +# with mesh.deform_mesh(): +# mesh.data[:] += vel_effMesh.data[:]*dt + + # particle population control + pop_control1.repopulate() + #pop_control2.repopulate() + #pop_control3.repopulate() + + if rank==0: + print('step=',step,'time=',timestep,'dt=',dt,'exec_time=',exec_time) + comm.Barrier() + + return timestep+dt, step+1 + + +# In[ ]: + + +while step -## Notes: +[![DOI](https://zenodo.org/badge/569971744.svg)](https://zenodo.org/badge/latestdoi/569971744) + + + +Launch this repository - +[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/underworld-community/sachau-et-al-ice-sheet/HEAD) + +Abstract +----- +Numerical models have become an indispensable tool for understanding and predicting the flow of ice +sheets and glaciers. Here we present the full-Stokes software +package Underworld to the glaciological community. The +code is already well established in simulating complex geodynamic systems. Advantages for glaciology are that it provides a full-Stokes solution for elastic–viscous–plastic materials and includes mechanical anisotropy. Underworld uses a +material point method to track the full history information of +Lagrangian material points, of stratigraphic layers and of free +surfaces. We show that Underworld successfully reproduces +the results of other full-Stokes models for the benchmark experiments of the Ice Sheet Model Intercomparison Project for +Higher-Order Models (ISMIP-HOM). Furthermore, we test +finite-element meshes with different geometries and highlight the need to be able to adapt the finite-element grid to +discontinuous interfaces between materials with strongly different properties, such as the ice–bedrock boundary + + +More details on this project can be seen [here](https://doi.org/10.5194/gmd-15-1-2022): +_Sachau, T., Yang, H., Lang, J., Bons, P.D. and Moresi, L., 2022. ISMIP-HOM benchmark experiments using Underworld. Geoscientific Model Development._ + + + +Files Description +----- + +File | Purpose +--- | --- +`Exp_A_3D.py` | 3D model for the Experiment A in Sachau_et_al_2022. +`Exp_B_2D.py` | 2D model for the Experiment B. +`Exp_B_2D.ipynb` | notebook of 2D model for the Experiment B. +`Exp_B_3D.py` | 3D model for the Experiment B. +`Exp_C_3D.py` | 3D model for the Experiment C. +`Exp_D_2D.py` | 2D model for the Experiment D. +`Exp_E_mixed-slip-version.py` | 2D model for the Experiment E with mixed slip. +`Exp_E_mixed-no-slip-version.py` | 2D model for the Experiment E without slip. +`Exp_F_3D.py` | 3D model for the Experiment F. +'velocity_10000.0.png' | image of velocity profile of Exp_B_2D. +'mesh_deform_default_swarm.png' | image of deformed mesh. +'Results-all-simulations.zip' | raw data of all simulations. +'Results-and-Figures.pdf' | figures used in Sachau et al. 2022. + +Tests +----- + +This study uses Underworld to reproduce the benchmark models provided by [ISMIP–HOM](https://doi.org/10.5194/tc-2-95-2008) + +_Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., De Smedt, B., Gagliardini, O., Gudmundsson, G.H., Hindmarsh, R.C., Hubbard, A., Johnson, J.V. and Kleiner, T., 2008. Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP–HOM). The Cryosphere, 2(2), pp.95-108._ + +Better to take notebook file Exp_B_2D.ipynb as a start. + +Parallel Safe +------------- +3D model results can be obtained in parallel operation. + + diff --git a/model_code_inputs/Results-all-simulations.zip b/model_code_inputs/Results-all-simulations.zip new file mode 100644 index 0000000000000000000000000000000000000000..4844440fa0d1dde34f351168e8a170728cf5a5d1 GIT binary patch literal 624409 zcmaG`RahKdu*5a6I0V;V!6CQ@_r=}aEx5b826uN|+}+(RxCGY#cmMm{=erNH^KfR* zOiyifb#*JsK*L}`{P)4unO6DVlm9#5fxm&K&aO5t&J2b&HVn>|wyrjYE|&Io&PPUF_|!gW{n}%e z@1Lwc>8YOdjul?%o$oo$6^JpG?iCAZJRSz6fFHLr)31k zGWD95o!vt@_+?qrdE6VxJxs*C+|jF^ zYw@_L5Lr(aiAwn~ELCD>+jV@HedUQ!K5@^o%t+)F5zPLe6YR;dl2RtoE#Eog~#I#;ge)msG7e0-VX!6du z*j~F5RqFVm7V{)&292IWD@MOHhC6L&c}+$mz^1L1ieAR}pOl4kIib_S&Crqbhjqhk zLk-Tb>r@su3{js&;Th8sk2&4HF}m``BkNevvjvn}X$E`2s|LnR1D)pcjnkl0YSee0 zx2W-_`?%9_zjD{;!}!V_((f+6jqIt`Yr2^id09r-jyPoI;CF9}E-K2`3r7 zMyijFe?F7XW@+*u7hgnQwaZOCOwJwN2*@9;Q#FbpK@U?+a>e;%hxOe 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