weno3_states.c

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#include "pluto.h"

static void WENO3_COEFF(double **, double **, double **, double **, Grid *);

/* ************************************************************* */
void States (const State_1D *state, int beg, int end, Grid *grid)
/* 
 *
 * PURPOSE
 *
 *   Provide a three-point stencil, third-order 
 *   reconstruction algorithm based on the WENO3.
 *
 *
 * LAST MODIFIED
 *
 *   Nov 3rd 2009
 *   by A. Mignone (mignone@ph.unito.it)
 *
 **************************************************************** */
{
  int    k, nv, i;
  double dmm, dx2;
  double **v, **vp, **vm, *dvp, *dvm, *dx;
  double **Lv, **Rv, *lambda;
  double *R, *L, *P, *M;
  double b0, S0, wp, tau;
  double b1, S1, wm;
  double dwp[NVAR], dwp_lim[NVAR];
  double dwm[NVAR], dwm_lim[NVAR];
  double dvpR, dvmR;
  static double **Rg, **Lg, **Pg, **Mg; /* -- interpolation coeffs -- */
  static double **dv;

/* -----------------------------------------------------
   0. Allocate memory and set pointer shortcuts
   ----------------------------------------------------- */
   
  if (dv == NULL) {
    dv = ARRAY_2D(NMAX_POINT, NVAR, double);
    Rg = ARRAY_2D(DIMENSIONS, NMAX_POINT, double);
    Lg = ARRAY_2D(DIMENSIONS, NMAX_POINT, double);
    Pg = ARRAY_2D(DIMENSIONS, NMAX_POINT, double);
    Mg = ARRAY_2D(DIMENSIONS, NMAX_POINT, double);
    WENO3_COEFF(Rg, Lg, Pg, Mg, grid);
  }

  v  = state->v;
  vp = state->vp;
  vm = state->vm;

#if RECONSTRUCT_4VEL
   ConvertTo4vel (state->v, beg-1, end+1);
#endif

  R  = Rg[g_dir]; L = Lg[g_dir];
  P  = Pg[g_dir]; M = Mg[g_dir];
  dx = grid[g_dir].dx;

/* ----------------------------------------------------
   1. compute slopes and left and right interface values 
   ---------------------------------------------------- */

  #if CHAR_LIMITING == NO  /* ----------------------------------------
                              a: Limiter on primitive variables
                              ----------------------------------------  */
   for (i = beg-1; i <= end; i++){
   for (nv = NVAR; nv--; ){
     dv[i][nv] = v[i+1][nv] - v[i][nv];
   }}

   for (i = beg; i <= end; i++){
     dvp = dv[i];  
     dvm = dv[i-1];

     #if SHOCK_FLATTENING == MULTID    
      if (state->flag[i] & FLAG_MINMOD){  
        for (nv = NVAR; nv--;    ) {
          dmm = MINMOD(dvp[nv], dvm[nv]);
          vp[i][nv] = v[i][nv] + 0.5*dmm;
          vm[i][nv] = v[i][nv] - 0.5*dmm;
        }
        continue;
      }
     #endif

     dx2 = dx[i]*dx[i];
     for (nv = 0; nv < NVAR; nv++){
       b0 = dvp[nv]*dvp[nv] + dx2;
       b1 = dvm[nv]*dvm[nv] + dx2;

       tau = dvp[nv] - dvm[nv];
       tau = tau*tau;

       S0 = 1.0 + tau/b0;
       S1 = 1.0 + tau/b1;
/*
S0 = 1.0/(b0 + 1.e-6)/(b0 + 1.e-6);
S1 = 1.0/(b1 + 1.e-6)/(b1 + 1.e-6);
       vp[nv] = v[i][nv] + (S0*dvp[nv] + 0.5*S1*dvm[nv])/(2.0*S0 + S1);
       vm[nv] = v[i][nv] - (S1*dvm[nv] + 0.5*S0*dvp[nv])/(2.0*S1 + S0);
*/

       vp[i][nv] = v[i][nv] + (S0*R[i]*dvp[nv] + P[i]*S1*R[i-1]*dvm[nv])
                             /(S0 + P[i]*S1);
       vm[i][nv] = v[i][nv] - (M[i]*S0*L[i]*dvp[nv] + S1*L[i-1]*dvm[nv])
                             /(M[i]*S0 + S1);

     }
   }       
  
  #else       /* --------------------------------------------
                 b: Limiter on characteristic variables
                 --------------------------------------------  */

   SoundSpeed2 (state->v, state->a2, state->h, beg, end, CELL_CENTER, grid);
   i = beg-1;
   for (nv = NVAR; nv--;   ) dv[i][nv] = v[i+1][nv] - v[i][nv];

   for (i = beg; i <= end; i++){

     NVAR_LOOP(nv) dv[i][nv] = v[i+1][nv] - v[i][nv];
     
     Lv = state->Lp[i];
     Rv = state->Rp[i]; 
     lambda = state->lambda[i];
     dvp = dv[i];   
     dvm = dv[i-1];
    
  /* -------------------------------
      project undivided differences 
      onto characteristic space
     ------------------------------- */
     
     PrimEigenvectors (v[i], state->a2[i], state->h[i], lambda, Lv, Rv);
     PrimToChar(Lv, dvp, dwp);
     PrimToChar(Lv, dvm, dwm);

     #if SHOCK_FLATTENING == MULTID    
      if (state->flag[i] & FLAG_MINMOD){  
        for (nv = NVAR; nv--;    ) {
          dmm = MINMOD(dvp[nv], dvm[nv]);
          vp[i][nv] = v[i][nv] + 0.5*dmm;
          vm[i][nv] = v[i][nv] - 0.5*dmm;
        }
        continue;
      }
     #endif

     dx2 = dx[i]*dx[i];
     for (k = NVAR; k--; ){
       b0 = dwp[k]*dwp[k] + dx2;
       b1 = dwm[k]*dwm[k] + dx2;

       tau = dwp[k] - dwm[k];
       tau = tau*tau;

       S0 = 1.0 + tau/b0;
       S1 = 1.0 + tau/b1;

       dwp_lim[k] = (S0*dwp[k] + 0.5*S1*dwm[k])/(2.0*S0 + S1);
       dwm_lim[k] = (S1*dwm[k] + 0.5*S0*dwp[k])/(2.0*S1 + S0);
/*
    dwp_lim[k] = (S0*R[i]*dwp[k] + P[i]*S1*R[i-1]*dwm[k])/(S0 + P[i]*S1);
    dwm_lim[k] = (M[i]*S0*L[i]*dwp[nv] + S1*L[i-1]*dwm[nv])/(M[i]*S0 + S1);
*/

     }
     for (nv = NFLX; nv--;   ){
       dvpR = dvmR = 0.0;
       #ifdef STAGGERED_MHD
        if (nv == BXn) continue;
       #endif
       for (k = NFLX; k--; ){
         dvpR += dwp_lim[k]*Rv[nv][k];
         dvmR += dwm_lim[k]*Rv[nv][k];
       }
       vp[i][nv] = v[i][nv] + dvpR;
       vm[i][nv] = v[i][nv] - dvmR;
     }

  /* -------------------------------------------------- 
      Passive scalars are treated in a separate loop
      since the characteristic structure is simpler,
      that is, L=R=diag(1) and the characteristic 
      variable coincides with the primitive one.
     -------------------------------------------------- */            

     #if NFLX != NVAR
      for (nv = NFLX; nv < NVAR; nv++ ){
        vp[i][nv] = v[i][nv] + dwp_lim[nv];
        vm[i][nv] = v[i][nv] - dwm_lim[nv];
      }
     #endif

   }
   
  #endif /* CHAR_LIMITING == YES */
   
/* --------------------------------------------------
   2. Ensure positivity of density and pressure 
   -------------------------------------------------- */

  for (i = beg; i <= end; i++){
    dvp = dv[i];  
    dvm = dv[i-1]; 
    if (vp[i][RHO] < 0.0 || vm[i][RHO] < 0.0){
      for (nv = NFLX; nv--;  ){
        dmm = MINMOD(dvp[RHO], dvm[RHO]);
        vp[i][RHO] = v[i][RHO] + 0.5*dmm;
        vm[i][RHO] = v[i][RHO] - 0.5*dmm;  
      }
    }

    #if HAVE_ENERGY
     if (vp[i][PRS] < 0.0 || vm[i][PRS] < 0.0){
       for (nv = NFLX; nv--;  ){
         dmm = MINMOD(dvp[PRS], dvm[PRS]);
         vp[i][PRS] = v[i][PRS] + 0.5*dmm;
         vm[i][PRS] = v[i][PRS] - 0.5*dmm;  
       }
     }
    #endif
    #if ENTROPY_SWITCH
     if (vp[i][ENTR] < 0.0 || vm[i][ENTR] < 0.0){
       dmm = MINMOD(dvp[ENTR], dvm[ENTR]);
       vp[i][ENTR] = v[i][ENTR] + 0.5*dmm;
       vm[i][ENTR] = v[i][ENTR] - 0.5*dmm;
     }
    #endif      

  /* -- Relativistic Limiter -- */

    #if PHYSICS == RHD || PHYSICS == RMHD
     VelocityLimiter (v[i], vp[i], vm[i]);
    #endif

  }

/* -------------------------------------------
   3. Shock flattening 
   -------------------------------------------  */

#if SHOCK_FLATTENING == ONED 
  Flatten (state, beg, end, grid);
#endif

/* -------------------------------------------
   4. Assign face-centered magnetic field
   -------------------------------------------  */

  #ifdef STAGGERED_MHD
   for (i = beg - 1; i <= end; i++) {
     state->vR[i][BXn] = state->vL[i][BXn] = state->bn[i];
   }
  #endif

/* --------------------------------------------------------
   5. Evolve L/R states and center value by dt/2
   -------------------------------------------------------- */

#if TIME_STEPPING == CHARACTERISTIC_TRACING
  CharTracingStep(state, beg, end, grid);
#elif TIME_STEPPING == HANCOCK
  HancockStep(state, beg, end, grid);
#endif

/* --------------------------------------------------------
   6. Convert back to 3-velocity
   -------------------------------------------------------- */

#if RECONSTRUCT_4VEL
  ConvertTo3vel (state->v, beg-1, end+1);
  ConvertTo3vel (state->vp, beg, end);
  ConvertTo3vel (state->vm, beg, end);  
#endif

/* ----------------------------------------------
   7. Obtain L/R states in conservative variables
   ---------------------------------------------- */

  PrimToCons (state->vp, state->up, beg, end);
  PrimToCons (state->vm, state->um, beg, end);
}

/* ************************************************************************* */
void WENO3_COEFF(double **R, double **L, double **P, double **M, Grid *grid)
/*
 *
 *
 *
 *
 **************************************************************************** */
{
  int  d, i, beg, end;
  double *dV;

  for (d = 0; d < DIMENSIONS; d++){
    dV = grid[d].dV;
    beg = 0; end = grid[d].np_tot - 2;
    for (i = beg; i <= end; i++){
      R[d][i] = dV[i + 1]/(dV[i] + dV[i + 1]);
      L[d][i] = 1.0 - R[d][i];
    }
    beg = 1; end = grid[d].np_tot - 2;
    for (i = beg; i <= end; i++){
      P[d][i] = dV[i + 1]/(dV[i] + dV[i - 1]);
      M[d][i] = dV[i - 1]/(dV[i] + dV[i + 1]);
    }
  }
}