aslamsharp.c

Aslam Extrapolations
- Results
- References

Aslam Extrapolations

We want to apply Aslam extrapolations on a field which is non-null just at the interface, described using a VOF field.

#include "grid/multigrid.h"
#include "utils.h"
#include "aslam.h"
#include "redistance.h"
#include "view.h"

We define the volume fraction field f, the function that we want to extrapolate m, and the Heaviside functions H which defines the extrapolation region (just for visualization).

scalar f[], m[], H[];

int main (void) {

We set the domain geometry and we initialize the grid and the volume fraction.

  X0 = -0.5, Y0 = -0.5;
  init_grid (1 << 6);
  fraction (f, (sq(0.4) - sq(x) - sq(y)));

We create two copies of the volume fraction fields.

  scalar fL[], fG[];
  foreach() {
    fL[] = f[];
    fG[] = 1. - f[];
  }

We convert the VOF field to a level set.

  scalar ls1[], ls2[];
  vof_to_ls (f, ls1);
  foreach()
    ls2[] = -ls1[];

The function to extrapolate is initialize to x*y just at the interface.

  foreach()
    m[] = (f[] > 1.e-10 && f[] < 1.-1.e-10) ? x*y : 0.;

We extrapolate m from the interface toward the gas phase.

  clear();
  draw_vof ("f", lw = 1.5);
  squares ("m", spread = -1);
  save ("initial.png");

We extrapolate m from the interface toward the liquid phase.

  constant_extrapolation (m, ls1, 0.5, 10, c=fL, nl=0,
      nointerface=true);

  clear();
  draw_vof ("f", lw = 1.5);
  squares ("m", spread = -1);
  save ("extrapolated1.png");
  fprintf (stderr, "constant = %g\n", statsf(m).sum);

We extrapolate m from the interface toward the liquid phase.

  foreach()
    m[] = (f[] > 1.e-10 && f[] < 1.-1.e-10) ? x*y : 0.;

  constant_extrapolation (m, ls2, 0.5, 10, c=fG, nl=0,
      nointerface=true);

  clear();
  draw_vof ("f", lw = 1.5);
  squares ("m", spread = -1);
  save ("extrapolated2.png");
  fprintf (stderr, "linear = %g\n", statsf(m).sum);

We print the Heaviside function used for these extrapolations. This function is non-null in the region where m must be extrapolated.

  mapregion (H, fL, nl=0, nointerface=true);

  clear();
  draw_vof ("f", lw = 1.5);
  squares ("H", spread = -1);
  save ("heaviside.png");
  fprintf (stderr, "heaviside = %g\n", statsf(H).sum);
}

Results

References

[aslam2004partial]

Tariq D Aslam. A partial differential equation approach to multidimensional extrapolation. Journal of Computational Physics, 193(1):349–355, 2004.