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[];
        phi[] = sq(0.25) - sq(x) - sq(y);

    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).

    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"
    Exact and VOF-reconstucted interface (script)

    Exact and VOF-reconstucted interface (script)