smoothMesh

OpenFOAM mesh smoothing tool to improve mesh quality. Moves internal mesh points by using the Centroidal smoothing algorithm (a version of the Laplacian smoothing algorithm, which uses surrounding cell centers instead of the neighbour point locations to calculate the new point position). Optional heuristic quality constraint options exist to constrain the smoothing, to avoid self-intersections. No changes to mesh topology are made.

Image below illustrates the need for restricting centroidal smoothing. Without quality constraints, centroidal smoothing would move the point highlighted in blue to the location highlighted with green, which is outside of the domain. Thereby, centroidal smoothing can create self-intersecting cells, depending on the geometry and topology of the mesh. Self-intersections can be avoided by using additional quality constraints, which restrict the movement of vertices.

Current features and restrictions

• Works on 3D polyhedron meshes
• Can be run in parallel
• Requires a consistent (not self-intersecting or tangled) initial mesh with "good enough" quality
• Smoothes internal mesh points
• NEW: Limited boundary point smoothing (work in progress, see options below)
• Optional handling of prismatic boundary layers
• Developed on OpenFOAM.com v2312, tested on v2412

Compilation instructions

. /usr/lib/openfoam/openfoam2412/etc/bashrc
cd smoothMesh/src
wclean; wmake

Command line options

Basic options

• -centroidalIters specifies the maximum number of smoothing iterations (default 1000).

• -relTol is the relative tolerance convergence criteria for stopping smoothing iterations (default 0.02). If residual (average length of point movement relative to maxStepLength) drops below this value, then smoothing is ended.

• -minEdgeLength defines edge length below which edge points are fully frozen at their current location. Freezing happens only if edge length would decrease during smoothing. Edge length is allowed to increase regardless of this value. If no value is provided, a default value of half the length of the shortest edge in the initial mesh is applied.

• -maxStepLength is the maximum length (in metres) for moving a point in one iteration. Smoothing process seems to be stable when this value is in the range 10% - 50% of the minimum cell side length. If no value is specified, a default value of 0.3 times the minEdgeLength is applied.

• -totalMinFreeze option causes mesh points on all edges shorter than -minEdgeLength to freeze, even if edge length would increase in smoothing (default false). This option is useful to keep boundary layers in the mesh unmodified, and smooth the large cells only, if the special boundary layer related options below are not used.

Quality constraint options

The following options are related to additional heuristic quality control constraints for smoothing. The constraints work by disallowing movement of point (freezing of points) if the movement would cause quality of the mesh to suffer too much. Without constraining, centroidal smoothing may squish cells and create self-intersecting cells e.g. near concave geometry features, depending on the mesh details. Have a look at the algorithm description document for details.

Note: The old -qualityControl option has been superceded by the options below.

• -edgeAngleConstraint boolean option enables an additional quality control which restricts decrease of smallest edge-edge angle below minAngle (default is true).

• -faceAngleConstraint boolean option enables an additional quality control which restricts decrease of smallest and largest face-face angle below minAngle and above maxAngle (default is true).

• -minAngle option defines the value for minimum angle (in degrees, default value 35).

• -maxAngle option specifies the value for maximum angle (in degrees, default value 160).

• Note: -minAngle value causes point freezing only if the minimum angle is below this value and if the minimum angle would decrease in smoothing. Points are allowed to move if the minimum angle value increases with smoothing, regardless of this value. The same applies for the -maxAngle option: Freezing takes place only if maximum angle is above the specified value and if the maximum angle would increase in smoothing.

Boundary layer related options

The options below are related to handling of prismatic cells near mesh boundaries, to either preserve or improve the orthogonality and the thickness of boundary layer cells in the mesh. If the mesh contains prismatic boundary layers, the unconstrained centroidal smoothing will tend to bloat the boundary layer cells into normal size. That can be avoided using the options below. These options affect only the prismatic cell edges near the mesh boundaries (see the algorithm description document for details).

Warning: This is an experimental feature!

• -boundaryMaxBlendingFraction is the maximum fraction (0 <= value <= 1) by which boundary layer edge length and edge direction are blended with the centroidal smoothing locations. Zero value disables the effect of all other boundary related variables below (default 0). Values like 0.3 or 0.8 seems to produce good results in practice.

• -boundaryEdgeLength specifies the target thickness for the first boundary layer cells (prismatic side edge length). If no value is provided, the value of minEdgeLength is applied.

• -boundaryExpansionRatio specifies the thickness ratio by which the boundary edge length is assumed to increase (default: 1.3).

• -boundaryMinLayers is an integer value specifying the number of boundary layers which experience a full force of boundary blending specified with the -boundaryMaxBlendingFraction option (default: 1).

• -boundaryMaxLayers specifies the number of boundary cell layers beyond which boundary blending options above ceases to affect smoothing, and only centroidal smoothing is applied (default: 4).

• -patches option can be used to limit the boundary layer treatment to specified patches only. You can specify one or several patches, optionally with wild cards. For example -patches 'walls' or -patches '( stator "rotor.*" )'. All patches are affected by default.

• -boundaryMaxPointBlendingFraction is the maximum fraction (0 <= value <= 1) by which boundary points are projected orthogonally to the boundary from the first layer prismatic points. Value like 0.8 seems to produce good results in practice. Note: Projection is made only if the boundary faces surrounding the boundary form a flat surface.

• -boundaryPointSmoothingPatches option can be used to limit the boundary point projection defined with the above option (-boundaryMaxPointBlendingFraction) to specified patches only. You can specify one or several patches, optionally with wild cards. For example -patches 'walls' or -patches '( stator "rotor.*" )'. All patches are affected by default.

Note: The combination of -boundaryMaxBlendingFraction and -boundaryMaxPointBlendingFraction gives different results, depending on the mesh and geometry. Figure below illustrates one example, showing a cross section in the middle of the mesh.

Description of the algorithm

Please view the algorithm description document.

Basic usage examples

You can run smoothMesh without providing any parameter values, but the result may not be very good, depending on your initial mesh. It is suggested to adjust at least the -centroidalIters, -relTol, -maxStepLength and -minEdgeLength options according to your case.

• Parallel run example: mpirun -np 3 smoothMesh -centroidalIters 100 -relTol 0.05 -maxStepLength 0.01 -minEdgeLength 0.05 -parallel

• Serial run example: smoothMesh -centroidalIters 100 -relTol 0.05 -maxStepLength 0.01 -minEdgeLength 0.05

Test case

The folder testcase contains an artificial test case which contains skewed and non-orthogonal cells, as well as variance in geometric cell shapes and topology. This is meant to be a challenging (but not impossible) task for centroidal smoothing.

Video of the smoothing process on a horizontal cross-section.

Figures below illustrate how smoothing can go wrong (or right), depending on the parameters applied.

This is the starting mesh:

Test 1 (bad results): No boundary layers, without faceAngleConstraint, produces self-intersections. Full command: smoothMesh -centroidalIters 100 -minEdgeLength 0.01 -maxStepLength 0.004 -faceAngleConstraint false

Test 2 (bad results): No boundary layers, too large minAngle does not allow much smoothing. Full command: smoothMesh -centroidalIters 100 -minEdgeLength 0.01 -maxStepLength 0.004 -minAngle 45 -maxAngle 160 -faceAngleConstraint true

Test 3 (good results): No boundary layers, faceAngleConstraint creates mesh without self-intersections. Full command: smoothMesh -centroidalIters 100 -minEdgeLength 0.01 -maxStepLength 0.004 -minAngle 15 -maxAngle 160 -faceAngleConstraint true

Test 4 (bad results): Boundary layers without patches specification creates boundary layers on outer walls. Full command: smoothMesh -centroidalIters 100 -minEdgeLength 0.01 -maxStepLength 0.004 -minAngle 15 -maxAngle 160 -faceAngleConstraint true -boundaryMaxBlendingFraction 0.8 -boundaryEdgeLength 0.01

Test 5 (good results): Boundary layers for patch named default, best result. Full command: smoothMesh -centroidalIters 100 -minEdgeLength 0.01 -maxStepLength 0.004 -minAngle 15 -maxAngle 160 -faceAngleConstraint true -boundaryMaxBlendingFraction 0.8 -boundaryEdgeLength 0.01 -patches '("def.*")'

Test 6 (bad results): Boundary layers for patch named default, too large boundaryEdgeLength. Full command: smoothMesh -centroidalIters 100 -minEdgeLength 0.01 -maxStepLength 0.004 -minAngle 15 -maxAngle 160 -faceAngleConstraint true -boundaryMaxBlendingFraction 0.8 -boundaryEdgeLength 0.025 -patches '("def.*")'

Getting help and feedback

Please use Github issues section for reporting bugs. If you like this tool, please star this repository in Github!

Link to discussion thread on CFD-Online for discussions

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