sphere-periodic-z.c

Sphere advected in the z-direction in a tri-periodic domain with DLMFD
Physical parameters
output and numerical parameters
Results
Animation

Sphere advected in the z-direction in a tri-periodic domain with DLMFD

A sphere twice as heavy as the surrounding fluid is advected in the z-direction by a pressure gradient

# define LEVEL 6 
# include "grid/octree.h"
# define DLM_Moving_particle 1

# define NPARTICLES 1

# define adaptive 1
# define MAXLEVEL (LEVEL + 1)

Physical parameters

# define Uc 1. //caracteristic velocity
# define rhoval 1. // fluid density
# define diam (1.) // particle diameter
# define ReD  200. // Reynolds number based on the particle's diameter
# define fs_density_ratio  2. // fluid solid density ratio
# define Ld_ratio 5. // box size-particle diameter ratio
# define Ldomain (Ld_ratio*diam)
# define rhosolid (fs_density_ratio*rhoval) //particle density
# define tval (rhoval*Uc*diam/ReD) //fluid dynamical viscosity

output and numerical parameters

# define Tc (diam/Uc) // caracteristic time scale
# define mydt (Tc/200) // maximum time-step (the time step is also adaptive in time but it won't exceed this value)
# define maxtime (1.5)
# define tsave (Tc/200.)

We include the ficitious-domain implementation with a toy-model granular solver

# include "dlmfd-toygs.h"
# include "view.h"

double deltau;
scalar un[];

int main() {
  L0 = Ldomain;

  /* set time step */
  DT = mydt;
  
  /* initialize grid */
  init_grid(1 << (LEVEL));
  
  /* boundary conditions: periodic everywhere */
  foreach_dimension() 
    periodic(top);

  /* Convergence criteria */
  TOLERANCE = 1e-3;
  
  run();
}

We initialize the fluid and particle variables.

event init (i = 0) {
  /* set origin */
  origin (0., 0., 0.);

  /* Initialize acceleration (face) vectors for pressure gradient to drive the flow */
  if (is_constant(a.x)) {
    a = new face vector;
    foreach_face()
      a.x[] = 0.;
    boundary ((scalar *){a});
  }
 
  /* fluid initial condition: */
  foreach() {
    foreach_dimension()
      u.x[] = 0;
    un[] = u.x[];
  }

  /* initial condition: particles position */
  particle * p = particles;
  
  for (int k = 0; k < NPARTICLES; k++) {
    GeomParameter gp;
    gp.center.x = L0/2;
    gp.center.y = L0/2;
    gp.center.z = L0-diam/2;
    gp.radius = diam/2;
    p[k].g = gp;
   
    /* initial condition: particle's velocity */
    coord c = {0., 0., 0.};
    p[k].U = c;
    p[k].w = c;
  }
}

We log the number of iterations of the multigrid solver for pressure and viscosity.

event logfile (i++) {
  deltau = change (u.x, un);
  fprintf (stderr, "log output %d %g %d %d %g %g %g\n", i, t, mgp.i, mgu.i, mgp.resa, mgu.resa, deltau);  
}


event acceleration(i++) {
  face vector av = a;
  coord dp = {0, 0., 20./L0/rhoval};
  foreach_face(){
    av.x[] = dp.x;
  }
}

event output_data (t += tsave; t < maxtime) {
  /* view (fov = 22.3366, quat = {0,0,0,1}, tx = -0.465283, ty = -0.439056, bg = {1,1,1}, width = 890, height = 862, samples = 1); */
  /* view (fov = 29.0823, quat = {-0.5,0.5,-0.5,0.5}, tx = 0.5, ty = 0.5, bg = {0.3,0.4,0.6}, width = 804, height = 748, samples = 1); */

  view (fov = 26.8568, quat = {-0.733356,-0.326189,0.262887,0.535427}, tx = -0.66604, ty = 0.560201, bg = {0.3,0.4,0.6}, width = 886, height = 810, samples = 1);
  stats statsvelox;
  statsvelox = statsf (u.z); 

  clear();
  box();
  squares ("u.z", n = {1,0,0}, alpha = L0/2, map = cool_warm, min = statsvelox.min, max = statsvelox.max);
  cells(n = {1,0,0}, alpha = L0/2);
  save ("movie.mp4");
}