# include # include # include # include # include # include "stokes_2d_exact.h" int main ( ); void uvp_stokes1_test ( ); void resid_stokes1_test ( ); void gnuplot_stokes1_test ( ); void uvp_stokes2_test ( ); void resid_stokes2_test ( ); void gnuplot_stokes2_test ( ); void uvp_stokes3_test ( ); void resid_stokes3_test ( ); void gnuplot_stokes3_test ( ); /******************************************************************************/ int main ( ) /******************************************************************************/ /* Purpose: stokes_2d_exact_test() tests stokes_2d_exact(). Licensing: This code is distributed under the MIT license. Modified: 24 January 2015 Author: John Burkardt */ { timestamp ( ); printf ( "\n" ); printf ( "stokes_2d_exact_test():\n" ); printf ( " C version\n" ); printf ( " Test stokes_2d_exact().\n" ); uvp_stokes1_test ( ); resid_stokes1_test ( ); gnuplot_stokes1_test ( ); uvp_stokes2_test ( ); resid_stokes2_test ( ); gnuplot_stokes2_test ( ); uvp_stokes3_test ( ); resid_stokes3_test ( ); gnuplot_stokes3_test ( ); /* Terminate. */ printf ( "\n" ); printf ( "S2DE_TEST\n" ); printf ( " Normal end of execution.\n" ); timestamp ( ); return 0; } /******************************************************************************/ void uvp_stokes1_test ( ) /******************************************************************************/ /* Purpose: UVP_STOKES1_TEST samples the solution #1. Licensing: This code is distributed under the MIT license. Modified: 24 January 2015 Author: John Burkardt */ { int n = 1000; double *p; int seed; double *u; double *v; double *x; double xy_hi; double xy_lo; double *y; printf ( "\n" ); printf ( "UVP_STOKES1_TEST\n" ); printf ( " Exact Stokes solution #1:\n" ); printf ( " Estimate the range of velocity and pressure\n" ); printf ( " using a region that is the unit square.\n" ); xy_lo = 0.0; xy_hi = 1.0; seed = 123456789; x = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); y = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); u = ( double * ) malloc ( n * sizeof ( double ) ); v = ( double * ) malloc ( n * sizeof ( double ) ); p = ( double * ) malloc ( n * sizeof ( double ) ); uvp_stokes1 ( n, x, y, u, v, p ); printf ( "\n" ); printf ( " Minimum Maximum\n" ); printf ( "\n" ); printf ( " U: %14.6g %14.6g\n", r8vec_min ( n, u ), r8vec_max ( n, u ) ); printf ( " V: %14.6g %14.6g\n", r8vec_min ( n, v ), r8vec_max ( n, v ) ); printf ( " P: %14.6g %14.6g\n", r8vec_min ( n, p ), r8vec_max ( n, p ) ); free ( p ); free ( u ); free ( v ); free ( x ); free ( y ); return; } /******************************************************************************/ void resid_stokes1_test ( ) /******************************************************************************/ /* Purpose: RESID_STOKES1_TEST samples the residual for solution #1. Licensing: This code is distributed under the MIT license. Modified: 24 January 2015 Author: John Burkardt */ { int n = 1000; double *pr; int seed; double *ur; double *vr; double *x; double xy_hi; double xy_lo; double *y; printf ( "\n" ); printf ( "RESID_STOKES1_TEST\n" ); printf ( " Exact Stokes solution #1:\n" ); printf ( " Sample the Stokes residuals\n" ); printf ( " using a region that is the unit square.\n" ); xy_lo = 0.0; xy_hi = 1.0; seed = 123456789; x = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); y = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); ur = ( double * ) malloc ( n * sizeof ( double ) ); vr = ( double * ) malloc ( n * sizeof ( double ) ); pr = ( double * ) malloc ( n * sizeof ( double ) ); resid_stokes1 ( n, x, y, ur, vr, pr ); printf ( "\n" ); printf ( " Minimum Maximum\n" ); printf ( "\n" ); printf ( " Ur: %14.6g %14.6g\n", r8vec_amin ( n, ur ), r8vec_amax ( n, ur ) ); printf ( " Vr: %14.6g %14.6g\n", r8vec_amin ( n, vr ), r8vec_amax ( n, vr ) ); printf ( " Pr: %14.6g %14.6g\n", r8vec_amin ( n, pr ), r8vec_amax ( n, pr ) ); free ( pr ); free ( ur ); free ( vr ); free ( x ); free ( y ); return; } /******************************************************************************/ void gnuplot_stokes1_test ( ) /******************************************************************************/ /* Purpose: GNUPLOT_STOKES1_TEST plots solution #1 on a regular grid. Licensing: This code is distributed under the MIT license. Modified: 24 January 2015 Author: John Burkardt */ { char header[255]; int n; double *p; double s; double *u; double *v; double *x; double x_hi; double x_lo; int x_num = 21; double *y; double y_hi; double y_lo; int y_num = 21; printf ( "\n" ); printf ( "GNUPLOT_STOKES1_TEST:\n" ); printf ( " Exact Stokes solution #1:\n" ); printf ( " Generate a Stokes velocity field on a regular grid.\n" ); printf ( " Store in GNUPLOT data and command files.\n" ); x_lo = 0.0; x_hi = 1.0; y_lo = 0.0; y_hi = 1.0; x = ( double * ) malloc ( x_num * y_num * sizeof ( double ) ); y = ( double * ) malloc ( x_num * y_num * sizeof ( double ) ); grid_2d ( x_num, x_lo, x_hi, y_num, y_lo, y_hi, x, y ); n = x_num * y_num; u = ( double * ) malloc ( n * sizeof ( double ) ); v = ( double * ) malloc ( n * sizeof ( double ) ); p = ( double * ) malloc ( n * sizeof ( double ) ); uvp_stokes1 ( n, x, y, u, v, p ); strcpy ( header, "stokes1" ); s = 4.0; stokes_gnuplot ( header, n, x, y, u, v, s ); free ( p ); free ( u ); free ( v ); free ( x ); free ( y ); return; } /******************************************************************************/ void uvp_stokes2_test ( ) /******************************************************************************/ /* Purpose: UVP_STOKES2_TEST samples the solution #2. Licensing: This code is distributed under the MIT license. Modified: 24 January 2015 Author: John Burkardt */ { int n = 1000; double *p; int seed; double *u; double *v; double *x; double xy_hi; double xy_lo; double *y; printf ( "\n" ); printf ( "UVP_STOKES2_TEST\n" ); printf ( " Exact Stokes solution #2:\n" ); printf ( " Estimate the range of velocity and pressure\n" ); printf ( " using a region that is the unit square.\n" ); xy_lo = 0.0; xy_hi = 1.0; seed = 123456789; x = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); y = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); u = ( double * ) malloc ( n * sizeof ( double ) ); v = ( double * ) malloc ( n * sizeof ( double ) ); p = ( double * ) malloc ( n * sizeof ( double ) ); uvp_stokes2 ( n, x, y, u, v, p ); printf ( "\n" ); printf ( " Minimum Maximum\n" ); printf ( "\n" ); printf ( " U: %14.6g %14.6g\n", r8vec_min ( n, u ), r8vec_max ( n, u ) ); printf ( " V: %14.6g %14.6g\n", r8vec_min ( n, v ), r8vec_max ( n, v ) ); printf ( " P: %14.6g %14.6g\n", r8vec_min ( n, p ), r8vec_max ( n, p ) ); free ( p ); free ( u ); free ( v ); free ( x ); free ( y ); return; } /******************************************************************************/ void resid_stokes2_test ( ) /******************************************************************************/ /* Purpose: RESID_STOKES2_TEST samples the residual for solution #1. Licensing: This code is distributed under the MIT license. Modified: 24 January 2015 Author: John Burkardt */ { int n = 1000; double *pr; int seed; double *ur; double *vr; double *x; double xy_hi; double xy_lo; double *y; printf ( "\n" ); printf ( "RESID_STOKES2_TEST\n" ); printf ( " Exact Stokes solution #2:\n" ); printf ( " Sample the Stokes residuals\n" ); printf ( " using a region that is the unit square.\n" ); xy_lo = 0.0; xy_hi = 1.0; seed = 123456789; x = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); y = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); ur = ( double * ) malloc ( n * sizeof ( double ) ); vr = ( double * ) malloc ( n * sizeof ( double ) ); pr = ( double * ) malloc ( n * sizeof ( double ) ); resid_stokes2 ( n, x, y, ur, vr, pr ); printf ( "\n" ); printf ( " Minimum Maximum\n" ); printf ( "\n" ); printf ( " Ur: %14.6g %14.6g\n", r8vec_amin ( n, ur ), r8vec_amax ( n, ur ) ); printf ( " Vr: %14.6g %14.6g\n", r8vec_amin ( n, vr ), r8vec_amax ( n, vr ) ); printf ( " Pr: %14.6g %14.6g\n", r8vec_amin ( n, pr ), r8vec_amax ( n, pr ) ); free ( pr ); free ( ur ); free ( vr ); free ( x ); free ( y ); return; } /******************************************************************************/ void gnuplot_stokes2_test ( ) /******************************************************************************/ /* Purpose: GNUPLOT_STOKES2_TEST plots solution #2 on a regular grid. Licensing: This code is distributed under the MIT license. Modified: 24 January 2015 Author: John Burkardt */ { char header[255]; int n; double *p; double s; double *u; double *v; double *x; double x_hi; double x_lo; int x_num = 21; double *y; double y_hi; double y_lo; int y_num = 21; printf ( "\n" ); printf ( "GNUPLOT_STOKES2_TEST:\n" ); printf ( " Exact Stokes solution #2:\n" ); printf ( " Generate a Stokes velocity field on a regular grid.\n" ); printf ( " Store in GNUPLOT data and command files.\n" ); x_lo = 0.0; x_hi = 1.0; y_lo = 0.0; y_hi = 1.0; x = ( double * ) malloc ( x_num * y_num * sizeof ( double ) ); y = ( double * ) malloc ( x_num * y_num * sizeof ( double ) ); grid_2d ( x_num, x_lo, x_hi, y_num, y_lo, y_hi, x, y ); n = x_num * y_num; u = ( double * ) malloc ( n * sizeof ( double ) ); v = ( double * ) malloc ( n * sizeof ( double ) ); p = ( double * ) malloc ( n * sizeof ( double ) ); uvp_stokes2 ( n, x, y, u, v, p ); strcpy ( header, "stokes2" ); s = 0.05; stokes_gnuplot ( header, n, x, y, u, v, s ); free ( p ); free ( u ); free ( v ); free ( x ); free ( y ); return; } /******************************************************************************/ void uvp_stokes3_test ( ) /******************************************************************************/ /* Purpose: UVP_STOKES3_TEST samples the solution #3. Licensing: This code is distributed under the MIT license. Modified: 11 February 2015 Author: John Burkardt */ { int n = 1000; double *p; int seed; double *u; double *v; double *x; double xy_hi; double xy_lo; double *y; printf ( "\n" ); printf ( "UVP_STOKES3_TEST\n" ); printf ( " Exact Stokes solution #3:\n" ); printf ( " Estimate the range of velocity and pressure\n" ); printf ( " using a region that is [-1,+1]x[-1,+1].\n" ); xy_lo = -1.0; xy_hi = +1.0; seed = 123456789; x = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); y = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); u = ( double * ) malloc ( n * sizeof ( double ) ); v = ( double * ) malloc ( n * sizeof ( double ) ); p = ( double * ) malloc ( n * sizeof ( double ) ); uvp_stokes3 ( n, x, y, u, v, p ); printf ( "\n" ); printf ( " Minimum Maximum\n" ); printf ( "\n" ); printf ( " U: %14.6g %14.6g\n", r8vec_min ( n, u ), r8vec_max ( n, u ) ); printf ( " V: %14.6g %14.6g\n", r8vec_min ( n, v ), r8vec_max ( n, v ) ); printf ( " P: %14.6g %14.6g\n", r8vec_min ( n, p ), r8vec_max ( n, p ) ); free ( p ); free ( u ); free ( v ); free ( x ); free ( y ); return; } /******************************************************************************/ void resid_stokes3_test ( ) /******************************************************************************/ /* Purpose: RESID_STOKES3_TEST samples the residual for solution #3. Licensing: This code is distributed under the MIT license. Modified: 11 February 2015 Author: John Burkardt */ { int n = 1000; double *pr; int seed; double *ur; double *vr; double *x; double xy_hi; double xy_lo; double *y; printf ( "\n" ); printf ( "RESID_STOKES3_TEST\n" ); printf ( " Exact Stokes solution #3:\n" ); printf ( " Sample the Stokes residuals\n" ); printf ( " using a region that is [-1,+1]x[-1,+1].\n" ); xy_lo = -1.0; xy_hi = +1.0; seed = 123456789; x = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); y = r8vec_uniform_ab_new ( n, xy_lo, xy_hi, &seed ); ur = ( double * ) malloc ( n * sizeof ( double ) ); vr = ( double * ) malloc ( n * sizeof ( double ) ); pr = ( double * ) malloc ( n * sizeof ( double ) ); resid_stokes3 ( n, x, y, ur, vr, pr ); printf ( "\n" ); printf ( " Minimum Maximum\n" ); printf ( "\n" ); printf ( " Ur: %14.6g %14.6g\n", r8vec_amin ( n, ur ), r8vec_amax ( n, ur ) ); printf ( " Vr: %14.6g %14.6g\n", r8vec_amin ( n, vr ), r8vec_amax ( n, vr ) ); printf ( " Pr: %14.6g %14.6g\n", r8vec_amin ( n, pr ), r8vec_amax ( n, pr ) ); free ( pr ); free ( ur ); free ( vr ); free ( x ); free ( y ); return; } /******************************************************************************/ void gnuplot_stokes3_test ( ) /******************************************************************************/ /* Purpose: GNUPLOT_STOKES3_TEST plots solution #3 on a regular grid. Licensing: This code is distributed under the MIT license. Modified: 11 February 2015 Author: John Burkardt */ { char header[255]; int n; double *p; double s; double *u; double *v; double *x; double x_hi; double x_lo; int x_num = 21; double *y; double y_hi; double y_lo; int y_num = 21; printf ( "\n" ); printf ( "GNUPLOT_STOKES3_TEST:\n" ); printf ( " Exact Stokes solution #3:\n" ); printf ( " Generate a Stokes velocity field on [-1,+1]x[-1,+1].\n" ); printf ( " Store in GNUPLOT data and command files.\n" ); x_lo = -1.0; x_hi = +1.0; y_lo = -1.0; y_hi = +1.0; x = ( double * ) malloc ( x_num * y_num * sizeof ( double ) ); y = ( double * ) malloc ( x_num * y_num * sizeof ( double ) ); grid_2d ( x_num, x_lo, x_hi, y_num, y_lo, y_hi, x, y ); n = x_num * y_num; u = ( double * ) malloc ( n * sizeof ( double ) ); v = ( double * ) malloc ( n * sizeof ( double ) ); p = ( double * ) malloc ( n * sizeof ( double ) ); uvp_stokes3 ( n, x, y, u, v, p ); strcpy ( header, "stokes3" ); s = 0.05; stokes_gnuplot ( header, n, x, y, u, v, s ); free ( p ); free ( u ); free ( v ); free ( x ); free ( y ); return; }