Computation of volume fractions from a levelset function

#include "grid/cartesian.h"
#include "fractions.h"

int main()
  origin (-0.5, -0.5);
  init_grid (32);

The interface is a circle centered on the origin and of radius 0.25. We chose this radius because it leads to degenerate cases where the interface intersects the grid exactly on vertices.

We initialise a levelset function on the vertices of the grid.

  vertex scalar φ[];
    φ[] = sq(0.25) - sq(x) - sq(y);
  boundary ({φ});

We then use this function to compute the corresponding volume and surface fractions.

  scalar c[];
  face vector s[];
  fractions (φ, c, s);

To check that this is correct, we draw the corresponding facets, reconstructed using either c and s (on stdout), or only c (on stderr).

  output_facets (c, stdout, s);
  output_facets (c, stderr);

This gives this figure where “exact” uses c and s and “VOF” uses only c.

Exact and VOF-reconstucted interface

Exact and VOF-reconstucted interface