Computation of volume fractions on a variable-resolution grid

    This test case is similar to fractions.c but with a refined band in the middle.

    #include "fractions.h"

    The refinement band is defined by this function.

    int main()
      origin (-0.5, -0.5);
      init_grid (16);
      refine (level == 4 && fabs (x) < 0.25);

    We use a circle of radius 0.3 and initialise the fractions.

      scalar c[];
      c.refine = c.prolongation = fraction_refine;
      face vector s[];
      solid (c, s, sq(0.3) - sq(x) - sq(y));

    Output the reconstruced facets and cells.

      output_facets (c, stdout, s);
      output_facets (c, stderr);
      FILE * fp = fopen ("cells", "w");
      output_cells (fp);
      fclose (fp);

    Finally, we reconstruct the interface and display the reconstructed facets only in the “halo cells”. This is a check of the consistency of the boundary conditions applied to \mathbf{n} and \alpha.

      vector n[];
      scalar alpha[];
      reconstruction (c, n, alpha);
      boundary ({n, alpha});
      coord p[2];
      for (int l = 0; l < depth(); l++)
        foreach_halo (prolongation, l) 
          foreach_child() {
            coord m = {n.x[],n.y[]};
    	if (facets (m, alpha[], p) == 2)
    	  fprintf (stderr, "halo %g %g\nhalo %g %g\nhalo\n", 
    		   x + p[0].x*Delta, y + p[0].y*Delta, 
    		   x + p[1].x*Delta, y + p[1].y*Delta);

    This gives this figure where “exact” uses c and s, “VOF” uses only c and “halo” is the halo cell reconstuction.

    set size ratio -1
    set key out
    plot 'cells' w l t '', 'out' w l t "exact", '< grep -v halo log' w l t "VOF", \
         '< grep halo log' u 2:3 w p t 'halo'
    Exact and VOF-reconstucted interface (script)

    Exact and VOF-reconstucted interface (script)