diff_v.c

Tutorial part 2: Variable diffusivity and an adaptive grid

Tutorial part 2: Variable diffusivity and an adaptive grid

Here the code from the more simple diffusion example is extended to use a variable diffusivity and an adaptive grid. Please note the note in the corresponding event.

Results:

The evolution of the scalar field s

The level of refinement

#include "diffusion.h"
#include "run.h" 

scalar s[];

int main() {
  L0 = 1 [0];
  DT = 0.05;
  run();
}

event init (t = 0) {
  foreach() 
    s[] = exp(-(sq(x - 0.5) + sq(y - 0.5))*10.); 
}

event mov (t += 0.1) {
  output_ppm (s, file = "s.mp4", n = 256, min = -1, max = 1);
  scalar lev[];
  foreach() 
    lev[] = level; //`level` is available in the grid iterator
  output_ppm (lev, file = "level.mp4", n = 256, max = 6);
}

event diff (i++) {
  dt = dtnext (DT);

We define a variable diffusivity field (kap) and call the boudary() function in order to ensure its proper definiton near resolutions boundaries and on the various lower levels. see this documentation page. Note for those who attended the tutorial: I originally forgot to include this important step…

  face vector kap[];
  foreach_face(x)
    kap.x[] = x/100.;
  foreach_face(y)
    kap.y[] = 0.;
  diffusion (s, dt, kap);
}

Adaptivity is switched on with this event:

event adapt (i++) 
  adapt_wavelet ({s}, (double[]){0.01}, 6);

event stop (t = 10);