-
Notifications
You must be signed in to change notification settings - Fork 59
/
fem2d_navier_stokes_cavity.html
265 lines (241 loc) · 8.23 KB
/
fem2d_navier_stokes_cavity.html
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
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
<html>
<head>
<title>
FEM2D_NAVIER_STOKES_CAVITY - "Cavity" Routines for FEM2D_NAVIER_STOKES
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM2D_NAVIER_STOKES_CAVITY <br> "Cavity" Routines for FEM2D_NAVIER_STOKES
</h1>
<hr>
<p>
<b>FEM2D_NAVIER_STOKES_CAVITY</b>
is a FORTRAN90 library which
supplies information defining a Navier-Stokes flow problem in a cavity.
The cavity is a square region that is 1 unit wide and 1 unit
high. The tangential velocity is specified to be 1 along the
top boundary, with a zero normal component. On all other parts
of the boundary, the velocity is specified to be zero.
</p>
<p>
To run the problem directly, you only need the user-supplied routines
in <b>cavity.f90</b>, the node data in <b>nodes6.txt</b>, and the
element data in <b>triangles6.txt</b>.
</p>
<p>
You compile and link the solver with <b>cavity.f90</b>, using
commands like:
<pre>
gfortran fem2d_navier_stokes.f90 cavity.f90
mv a.out channel
</pre>
and then run the program with the command
<pre>
./cavity nodes6.txt triangles6.txt
</pre>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/fem2d_navier_stokes/fem2d_navier_stokes.html">
FEM2D_NAVIER_STOKES</a>,
a FORTRAN90 program which
solves the 2D incompressible Navier-Stokes equations in an
arbitrary triangulated region.
In order to run, it requires
user-supplied routines that define problem data.
</p>
<p>
<a href = "../../f_src/fem2d_navier_stokes_channel/fem2d_navier_stokes_channel.html">
FEM2D_NAVIER_STOKES_CHANNEL</a>,
a FORTRAN90 library which
contains the user-supplied routines necessary to run <b>fem2d_navier_stokes</b>
on the "channel" problem.
</p>
<p>
<a href = "../../f_src/fem2d_navier_stokes_inout/fem2d_navier_stokes_inout.html">
FEM2D_NAVIER_STOKES_INOUT</a>,
a FORTRAN90 library which
contains the user-supplied routines necessary to run <b>fem2d_navier_stokes</b>
on the "inout" problem.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "cavity.f90">cavity.f90</a>,
the user-supplied routines to evaluate the right hand side
and boundary conditions;
</li>
<li>
<a href = "cavity.sh">cavity.sh</a>,
commands to compile the user routines, link them with
the partial program, and run the program;
</li>
<li>
<a href = "cavity_output.txt">cavity_output.txt</a>,
output from a run of the program;
</li>
</ul>
</p>
<p>
The geometry is defined by sets of nodes and triangles.
The velocities use the full set of nodes,
and quadratic (6 node) triangles.
<ul>
<li>
<a href = "nodes6.txt">nodes6.txt</a>,
a text file containing the velocity nodes;
</li>
<li>
<a href = "nodes6.png">nodes6.png</a>,
a PNG image of
the velocity nodes;
</li>
<li>
<a href = "triangles6.txt">triangles6.txt</a>,
the quadratic triangulation;
</li>
<li>
<a href = "triangles6.png">triangles6.png</a>,
a PNG image of
the order 6 triangulation;
</li>
</ul>
</p>
<p>
The pressures are associated with a subset of the nodes
called "pressure nodes", and linear (3 node) triangles.
Note that, in the order 3 triangulation, the nodes are renumbered,
and do NOT inherit the labels used in the order 6 triangulation.
<ul>
<li>
<a href = "nodes3.txt">nodes3.txt</a>,
a text file containing the pressure nodes;
</li>
<li>
<a href = "nodes3.png">nodes3.png</a>,
a PNG image of
the pressure nodes;
</li>
<li>
<a href = "triangles3.txt">triangles3.txt</a>,
the linear triangulation;
</li>
<li>
<a href = "triangles3.png">triangles3.png</a>,
a PNG image of
the linear triangulation;
</li>
</ul>
</p>
<p>
The Stokes equations are solved first, providing the solution of
a linear system that can be used as a good estimate of the solution,
especially for high values of the viscosity.
<ul>
<li>
<a href = "stokes_pressure3.txt">stokes_pressure3.txt</a>,
a text file containing the Stokes pressure P at each linear node;
</li>
<li>
<a href = "stokes_pressure3.png">stokes_pressure3.png</a>,
a PNG image of
a contour plot of the Stokes pressure, produced by
<a href =
"../../m_src/triangulation_order3_contour/triangulation_order3_contour.html">
TRIANGULATION_ORDER3_CONTOUR</a>.
</li>
<li>
<a href = "stokes_velocity6.txt">stokes_velocity6.txt</a>,
a text file containing the Stokes velocity (U,V) at each velocity node;
</li>
<li>
<a href = "stokes_velocity6_dir.png">stokes_velocity6_dir.png</a>,
a PNG image of
the Stokes velocity direction field, created by
<a href = "../../f_src/vector_plot/vector_plot.html">
VECTOR_PLOT.</a>
</li>
<li>
<a href = "stokes_velocity6_vec.png">stokes_velocity6_vec.png</a>,
a PNG image of
the Stokes velocity field, created by
<a href = "../../f_src/vector_plot/vector_plot.html">
VECTOR_PLOT.</a>
</li>
<li>
<a href = "stokes_velocity6_arrows.png">stokes_velocity6_arrows.png</a>,
a PNG image of the Stokes velocity field, created by
<a href = "../../m_src/velocity_arrows/velocity_arrows.html">
VELOCITY_ARROWS.</a>
</li>
</ul>
</p>
<p>
The nonlinear Navier Stokes equations are solved, using
the Stokes solution as a starting point.
<ul>
<li>
<a href = "navier_stokes_pressure3.txt">
navier_stokes_pressure3.txt</a>,
a text file containing the Navier Stokes pressure P at each
pressure node;
</li>
<li>
<a href = "navier_stokes_pressure3.png">
navier_stokes_pressure3.png</a>,
a PNG image of
a contour plot of the Navier Stokes pressure, produced by
<a href =
"../../m_src/triangulation_order3_contour/triangulation_order3_contour.html">
TRIANGULATION_ORDER3_CONTOUR</a>.
</li>
<li>
<a href = "navier_stokes_velocity6.txt">
navier_stokes_velocity6.txt</a>,
a text file containing the Navier Stokes velocity (U,V)
at each velocity node;
</li>
<li>
<a href = "navier_stokes_velocity6_dir.png">
navier_stokes_velocity6_dir.png</a>,
a PNG image of
the Navier Stokes velocity direction field, created by
<a href = "../../f_src/vector_plot/vector_plot.html">
VECTOR_PLOT.</a>
</li>
<li>
<a href = "navier_stokes_velocity6_vec.png">navier_stokes_velocity6_vec.png</a>,
a PNG image of
the Navier Stokes velocity field, created by
<a href = "../../f_src/vector_plot/vector_plot.html">
VECTOR_PLOT.</a>
</li>
<li>
<a href = "navier_stokes_velocity6_arrows.png">navier_stokes_velocity6_arrows.png</a>,
a PNG image of the Navier Stokes velocity field, created by
<a href = "../../m_src/velocity_arrows/velocity_arrows.html">
VELOCITY_ARROWS.</a>
</li>
</ul>
</p>
<hr>
<i>
Last revised on 28 December 2010
</i>
<!-- John Burkardt -->
</body>
</html>