sandbox/alimare/level_set.h

    Level-Set events

    The level-set method relies on the use of \phi a higher-dimensional function, whose zero level-set \Gamma (which is a hypersurface) is an interface between two fluides.

    In our cases, \phi is initialized as a signed distance function.

    The level set function is defined and initialized elsewhere (typically by the user), the face vector field uf and the timestep dt are defined by a solver.

    The interface is advected using: \partial_t\phi+\mathbf{u_f}\cdot\nabla \phi=0 where \mathbf{u_f} is the velocity field and \phi is the level set function.

    In this pointer we store the different components of \mathbf{u_f}

    scalar TL[], TS[], dist[];
vector vpc[],vpcf[];

scalar * tracers    = {TL};
scalar * tracers2 = {TS};

scalar * level_set  = {dist};
face vector muv[];
mgstats mgT;
double DT_LS;
int itrecons= 30;
double tolrecons = 1.e-10;
int     nb_cell_NB  ;  // number of cells for the NB
double  NB_width ;     // length of the NB


double  latent_heat = 1.;
double  lambda[2] = {1.,1.}; // thermal capacity of each material
double epsK , epsV;
double eps4;
double T_eq = 0.;

scalar curve[];

    These variables will be the different parameters for our level-set method. NB stands for Narrow Band which is an approximation introduced by Adalsteinsson and Sethian, 1995.

    #define LS_face_value(a,i)      ((a[i] + a[i-1])/2.)

    I use a few personal functions in the other level-set related functions.

    #include "alex_functions.h"

    This set of functions helps you extrapolate the value of the distance beyond a wall

    foreach_dimension()
double distBeyondWall_x(Point point, scalar dist,int sign){
  double delt = dist[sign] - dist[];
  return sign2(delt)*sq(delt)/Delta;
}


#if TREE
event defaults (i = 0) {
  for (scalar s in tracers){
    s.refine = s.prolongation = refine_embed_linear;
    s.restriction = restriction_embed_linear;
  }
  for (scalar s in tracers2){
    s.refine = s.prolongation = refine_embed_linear2;
    s.restriction = restriction_embed_linear2;
  }
}
#endif


#if EMBED

    Inverts cs and fs fields.

    void invertcs(scalar cs, face vector fs){
  foreach(){
    cs[]      = 1.-cs[];
  }
  foreach_face(){
    fs.x[]      = 1.-fs.x[];
  }

  boundary({cs});
  restriction({cs});
  fractions_cleanup(cs,fs);
}

    Level-set function to volume and face fractions

    struct LS2frac{
  scalar dist;
  scalar cs;
  face vector fs;
  double s_clean;
};

void LS2fractions(struct LS2frac p){
  scalar dist = p.dist;
  scalar cs = p.cs;
  face vector fs = p.fs;
  double s_clean = p.s_clean;

  vertex scalar distn[];
  cell2node(dist,distn);
  fractions (distn, cs, fs);
  fractions_cleanup(cs,fs,smin = s_clean, opposite = true);

  boundary({cs});
  restriction({cs});
}
#endif
    [Adalsteinsson1995]

    David Adalsteinsson and James A Sethian. A fast level set method for propagating interfaces. Journal of computational physics, 118(2):269–277, 1995.