advect-sphere-mpi.c

Advection of a front-tracking mesh in MPI
- Results

Advection of a front-tracking mesh in MPI

In this file we test the advection of a capsule described by a Lagrangian mesh across a periodic boundary using 4 processors.

This is a test for capsule-ft-mpi.h.

#define LEVEL 6
#define LAG_LEVEL 4
#define RADIUS .125
#define L0 1.
#define T_END 1.

#include "grid/octree.h"
#include "navier-stokes/centered.h"
#include "lagrangian_caps/capsule-ft.h"
#include "lagrangian_caps/common-shapes-ft.h"
#include "lagrangian_caps/view-ft.h"

int main(int argc, char* argv[]) {
  origin(-.5*L0, -.5*L0, -.5*L0);
  N = 1 << LEVEL;
  init_grid(N);
  periodic(left);
  TOLERANCE = HUGE;
  stokes = true;
  DT = 5.e-3;
  run();
}

coord* ref_data = NULL;
event init (i = 0) {
  activate_spherical_capsule(&CAPS(0), level = LAG_LEVEL, radius = RADIUS);
  ref_data = malloc(CAPS(0).nln*sizeof(coord));
  for(int i=0; i<CAPS(0).nln; i++)
    foreach_dimension() ref_data[i].x = CAPS(0).nodes[i].pos.x;
}

event impose_u (i++) {
  foreach() {
    double x0 = x + L0 -t*L0*T_END;
    double y0 = y + L0;
    double a = -2*sq(sin(pi*x0))*sin(pi*y0)*cos(pi*y0)*cos(pi*t/T_END);
    double b = -2*sin(pi*x0)*cos(pi*x0)*sq(cos(pi*y0))*cos(pi*t/T_END);
    double theta = pi/4.;
    u.x[] = a*cos(theta)/2 + L0*T_END;
    u.y[] = b/2;
    u.z[] = a*sin(theta)/2;
  }
}

event adapt (i++) {
  tag_ibm_stencils(&CAPS(0));
  adapt_wavelet({stencils}, (double []){1.e-2}, maxlevel = LEVEL);
  generate_lag_stencils(&CAPS(0));
}

We compute the time evolutions of the normalized area and volume of the capsule

event progress_output (i++) {
  if (pid() == 0) {
    comp_triangle_area_normals(&CAPS(0));
    double narea = 0;
    for(int j=0; j<CAPS(0).nlt; j++) narea += CAPS(0).triangles[j].area;
    narea /= 4*pi*sq(RADIUS);
    comp_volume(&CAPS(0));
    double nvolume = CAPS(0).volume/CAPS(0).initial_volume;
    fprintf(stderr, "%d, %.5g, %.5g, %.5g, %.5g %.5g\n", i, t, narea, nvolume,
    CAPS(0).centroid.x, CAPS(0).initial_volume);
    fflush(stderr);
  }
}

event movie (i+=5) {
  view(fov = 25, bg = {1,1,1}, theta = 5*pi/6, psi = 0., phi = pi/8);
  clear();
  draw_lag(&CAPS(0), lw = .5, edges = true, facets = true);
  cells(n = {0,0,1});
  save("advected_sphere_mpi.mp4");
}

At the end of the simulation, we also compare the position of the membrane to its initial position. With an asymptotically fine space and time resolutions, they would coincide.

event output (t = T_END) {
  if (pid() == 0) {
    double avg_err, max_err;
    avg_err = 0.; max_err = -HUGE;
    for(int i=0; i < CAPS(0).nln; i++){
    double err = 0.;
    foreach_dimension() err += sq(GENERAL_1DIST(ref_data[i].x,
        CAPS(0).nodes[i].pos.x));
    err = sqrt(err);
    avg_err += err;
    if (err > max_err) max_err = err;
    }
    avg_err /= CAPS(0).nln;
    fprintf(stderr, "%.3g, %.3g\n", avg_err, max_err);
    fflush(stderr);
  }
}

event end (t = T_END) {
  free(ref_data);
  return 0;
}

Results

Movie of an advected sphere