fracface.h

Face fractions from reconstructed interface

Face fractions from reconstructed interface

#include "geometry.h"
#define VTOL 1.e-6

The function below return the face fraction sf.x at the selected cell face. As it is done for the sweep_x() function of vof.h, we use the operator foreach_dimension() to automatize the derivation of the functions in the other dimensions. Once the dimension is selected (x, y or z), the boolean variable right allows to select the face. If it is TRUE the face selected is that separating the cells [] and [1]. If FALSE the one returned is that between cells [] and [-1].

foreach_dimension()
static double interface_fraction_x (coord m, double alpha, bool right)
{
#if dimension == 2
  alpha += (m.x + m.y)/2;
  coord n = m;
  double xo = (right ? 1. : 0.);
  if (n.y < 0.) {
    alpha -= n.y;
    n.y = - n.y;
  }
  if (n.y < 1e-4)
    return (n.x*(right ? 1 : -1) < 0. ? 1. : 0.);
  return clamp((alpha - n.x*xo)/n.y, 0., 1.);
#else

#endif  
}

A unique value of the face fraction is calculated from the reconstructed interfaces at the cells sharing the face by averaging as shown below,

A unique value of the face fraction s is calculated by averaging, s = \sqrt{vleft \times vright}

void face_fraction (scalar f, face vector s)
{
  boundary({f});

We compute the normal vector in each cell to apply boundary to the vector field in order to get consistent values in the ghost cells.

  vector normal_vector[];
  foreach() {
    coord m = mycs (point, f);
    foreach_dimension() 
      normal_vector.x[] = m.x;
  }
  boundary((scalar*){normal_vector});

  foreach_face() {
    if (f[-1] < VTOL || f[] < VTOL) // some cell is empty
      s.x[] = 0.;
    else if (f[-1] > 1.- VTOL && f[] > 1.- VTOL) // both cells are full
      s.x[] = 1.;
    else {
      double vleft = 1., vright = 1.;
      if (f[] < 1. - VTOL) {
        coord m;
        foreach_dimension()
          m.x = normal_vector.x[];
        double alpha = plane_alpha (f[], m);
        vleft = interface_fraction_x (m, alpha, false);
      }
      if (f[-1] < 1. - VTOL) {
        coord m;
        foreach_dimension()
          m.x = normal_vector.x[-1];
        double alpha = plane_alpha (f[-1], m);
        vright = interface_fraction_x (m, alpha, true);
      }
      s.x[] = sqrt(vleft*vright);
    }
  }
}