forked from cedrict/fieldstone
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathbenchmark_sinking_block.tex
201 lines (159 loc) · 6.77 KB
/
benchmark_sinking_block.tex
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
\begin{flushright} {\tiny {\color{gray} benchmark\_sinking\_block.tex}} \end{flushright}
\vspace{1cm}
\begin{flushright}
Data pertaining to this section are to be found at:
\url{https://github.com/cedrict/fieldstone/tree/master/images/sinking_block}
\end{flushright}
\vspace{1cm}
The domain is a unit square. Fluids are such that
$\rho_1=1$, $\eta_1=1$ and $\rho_2=1.01$, $\eta_2=1000$.
Boundary conditions are either free slip or no slip on all sides.
Pressure is normalised so that the volume average is zero.
Gravity points downwards with $|\vec{g}|=1$.
Profile measurements are carried out on the dashed line.
\begin{center}
\input{tikz/tikz_sinking_block}
\end{center}
When using \aspect{}, it is good to remember that a compositional field is used,
which 'lives' on the nodes of the FE grid. Partof the input file is shown here:
\begin{verbatim}
subsection Compositional fields
set Number of fields = 1
end
subsection Initial composition model
set Model name = function
subsection Function
set Variable names = x,y
set Function constants = p=0.5
set Function expression = if(abs(x-p)<0.0625 && abs(y-p)<0.0625 , 1, 0)
end
end
subsection Material model
subsection Simple model
set Density differential for compositional field 1 = 0.01
set Composition viscosity prefactor = 1000
end
end
\end{verbatim}
The value of the composition (and therefore
the density and viscosity values) on a quadrature point is obtained via interpolation
and averaging, which is different than the Stone codes where the density
and viscosity are elemental quantities.
\newpage
%...................................................................
\paragraph{Free-slip boundary conditions}.
\begin{center}
\includegraphics[width=5.cm]{images/sinking_block/FS/stone93/grid}
\includegraphics[width=5.cm]{images/sinking_block/FS/stone93/u}
\includegraphics[width=5.cm]{images/sinking_block/FS/stone93/vel}\\
\includegraphics[width=5.cm]{images/sinking_block/FS/stone93/v}
\includegraphics[width=5.cm]{images/sinking_block/FS/stone93/press}
\includegraphics[width=5.cm]{images/sinking_block/FS/stone93/sr}\\
{\captionfont Results obtained with Stone 93.}
\end{center}
\begin{center}
\includegraphics[width=5.6cm]{images/sinking_block/u_FS}
\includegraphics[width=5.6cm]{images/sinking_block/v_FS}
\includegraphics[width=5.6cm]{images/sinking_block/pressure_FS}\\
\includegraphics[width=5.6cm]{images/sinking_block/v_FS_zoom}
\includegraphics[width=5.6cm]{images/sinking_block/pressure_FS_zoom}\\
\end{center}
\begin{center}
\includegraphics[width=7cm]{images/sinking_block/v_FS_ASPECT_56789}
\includegraphics[width=7cm]{images/sinking_block/pressure_FS_ASPECT_56789}\\
{\captionfont \aspect{} results with various global mesh refinement. No averaging}
\end{center}
\begin{center}
\includegraphics[width=7cm]{images/sinking_block/v_FS_ASPECT_avrg}
\includegraphics[width=7cm]{images/sinking_block/pressure_FS_ASPECT_avrg}\\
{\captionfont \aspect{} results with various averagings. level 9.}
\end{center}
\begin{center}
\begin{tabular}{llp{4cm}p{4cm}}
\hline
& & FS & NS \\
\hline\hline
$\min(u)$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$) & & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & & \\
\hline
$\max(u)$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$)& & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & & \\
\hline
$\min(v)$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$)& & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & \\
\hline
$\max(v)$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$)& & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & & \\
\hline
$\max(|v|)$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$)& & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & & \\
\hline
$v_{rms}$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$)& & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & \\
\hline
$\min(p)$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$)& & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & \\
\hline
$\max(p)$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$)& & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & & \\
\hline
$|v|(0.5,0.5)$ & Stone 18 ($Q_2\times Q_1$) & & \\
& Stone 93 ($P_2^+\times P_{-1}$)& & \\
& Stone 76 ($Q_2\times P_{-1}$) & & \\
& Aspect & & \\
\hline
\end{tabular}
\end{center}
Using error extrapolation (see Section~\ref{ss:extrapolation}), one can compute an
estimate of the resolution independent value of the vrms of maximum velocity for example:
\begin{center}
\includegraphics[width=5cm]{images/sinking_block/vrms_FS}
\includegraphics[width=5cm]{images/sinking_block/vrms_FS_extrapolation_rate}
\includegraphics[width=5cm]{images/sinking_block/vrms_FS_error}\\
\includegraphics[width=5cm]{images/sinking_block/maxvel_FS}
\includegraphics[width=5cm]{images/sinking_block/maxvel_FS_extrapolation_rate}
\includegraphics[width=5cm]{images/sinking_block/maxvel_FS_error}
\end{center}
We find that the rates are near unity.
TODO: write material model in ASPECT to bypass compositions!
\newpage
%......................................................................................
\paragraph{No-slip boundary conditions}.
\begin{center}
\includegraphics[width=5.6cm]{images/sinking_block/u_NS}
\includegraphics[width=5.6cm]{images/sinking_block/v_NS}
\includegraphics[width=5.6cm]{images/sinking_block/pressure_NS}
\end{center}
\begin{center}
\includegraphics[width=7cm]{images/sinking_block/v_NS_ASPECT_56789}
\includegraphics[width=7cm]{images/sinking_block/pressure_NS_ASPECT_56789}\\
{\captionfont ASPECT results with various global mesh refinement. No averaging}
\end{center}
\begin{center}
\includegraphics[width=7cm]{images/sinking_block/v_NS_ASPECT_avrg}
\includegraphics[width=7cm]{images/sinking_block/pressure_NS_ASPECT_avrg}\\
{\captionfont ASPECT results with various averagings. level 9.}
\end{center}
\begin{center}
\includegraphics[width=5.7cm]{images/sinking_block/NS/ASPECT/q2q1/eta}
\includegraphics[width=5.7cm]{images/sinking_block/NS/ASPECT/q2q1/vel}
\includegraphics[width=5.7cm]{images/sinking_block/NS/ASPECT/q2q1/sr}\\
{\captionfont Obtained with ASPECT, level 9.}
\end{center}
TODO: finish analysis