# 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 phi[];
foreach_vertex()
phi[] = sq(0.25) - sq(x) - sq(y);
boundary ({phi});

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

  scalar c[];
face vector s[];
fractions (phi, 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.

set size ratio -1
set key out
plot 'out' w l t "exact", 'log' w l t "VOF"