VlasovUpwind.c File Reference

Contains functions to compute the upwind flux at grid interfaces for the Vlasov equations. More...

#include <stdlib.h>
#include <math.h>
#include <basic.h>
#include <arrayfunctions.h>
#include <mathfunctions.h>
#include <physicalmodels/vlasov.h>
#include <hypar.h>

Go to the source code of this file.

Functions
double	VlasovAdvectionCoeff (int *, int, void *)
int	VlasovUpwind (double *fI, double *fL, double *fR, double *uL, double *uR, double *u, int dir, void *s, double t)

Detailed Description

Contains functions to compute the upwind flux at grid interfaces for the Vlasov equations.

Author

John Loffeld

Definition in file VlasovUpwind.c.

Function Documentation

double VlasovAdvectionCoeff	(	int *	idx,
		int	dir,
		void *	s
	)

Returns the advection coefficient at a given grid index \(c\), where

\begin{equation} c = v_i, \end{equation}

if dir < Vlasov::ndims_x ( \(i = {\rm dir}\)), and

\begin{equation} c = E_i, \end{equation}

the electric field if dir >= Vlasov::ndims_x ( \(i = \) dir-Vlasov::ndims_x).

Note: this function assumes that the electric field has already been set.

Parameters

idx	grid index
dir	Spatial dimension
s	Solver object of type HyPar

Definition at line 28 of file VlasovAdvectionCoeff.c.

{

  HyPar  *solver = (HyPar*)  s;
  Vlasov *param  = (Vlasov*) solver->physics;

  int* dim    = solver->dim_local;
  int  ghosts = solver->ghosts;

  double retval = DBL_MAX;

  if (dir < param->ndims_x) {

    int veldim = dir + param->ndims_x;
    _GetCoordinate_(veldim,idx[veldim],dim,ghosts,solver->x,retval);

  }  else {

    int ndims_x = param->ndims_x;
    int dim_x[ndims_x]; _ArrayCopy1D_(dim, dim_x, ndims_x);

    int idx_x[ndims_x];
    _ArrayCopy1D_(idx, idx_x, ndims_x);
    int p; _ArrayIndex1D_(ndims_x, dim_x, idx_x, ghosts, p);
    retval = param->e_field[ndims_x*p+(dir-ndims_x)];
    
  }

  return retval;

}

int VlasovUpwind	(	double *	fI,
		double *	fL,
		double *	fR,
		double *	uL,
		double *	uR,
		double *	u,
		int	dir,
		void *	s,
		double	t
	)

Upwinding scheme for the Vlasov equations

Parameters

fI	Computed upwind interface flux
fL	Left-biased reconstructed interface flux
fR	Right-biased reconstructed interface flux
uL	Left-biased reconstructed interface solution
uR	Right-biased reconstructed interface solution
u	Cell-centered solution
dir	Spatial dimension
s	Solver object of type HyPar
t	Current solution time

Definition at line 17 of file VlasovUpwind.c.

{
  HyPar  *solver = (HyPar*)  s;
  Vlasov *param  = (Vlasov*) solver->physics;
  int    done;

  int ndims   = solver->ndims;
  int *dim    = solver->dim_local;
  int ghosts  = solver->ghosts;

  int index_outer[ndims], 
      index_inter[ndims], 
      bounds_outer[ndims], 
      bounds_inter[ndims];
  _ArrayCopy1D_(dim,bounds_outer,ndims); bounds_outer[dir] =  1;
  _ArrayCopy1D_(dim,bounds_inter,ndims); bounds_inter[dir] += 1;

  done = 0; _ArraySetValue_(index_outer,ndims,0);
  while (!done) {
    _ArrayCopy1D_(index_outer,index_inter,ndims);
    for (index_inter[dir] = 0; index_inter[dir] < bounds_inter[dir]; index_inter[dir]++) {

      int p; _ArrayIndex1D_(ndims,bounds_inter,index_inter,0,p);
      int indexL[ndims]; _ArrayCopy1D_(index_inter,indexL,ndims); indexL[dir]--;
      int indexR[ndims]; _ArrayCopy1D_(index_inter,indexR,ndims);
      int idxL[ndims], idxR[ndims];

      int neig = 2+4*(ndims-1);
      double eig[neig];
      int count = 0;
      eig[count] = VlasovAdvectionCoeff(indexL, dir, solver); count++;
      eig[count] = VlasovAdvectionCoeff(indexR, dir, solver); count++;
      for (int tdir = 0; tdir < ndims; tdir++ ) {
        if (tdir != dir) {
          _ArrayCopy1D_(indexL, idxL, ndims); idxL[tdir]--;
          _ArrayCopy1D_(indexR, idxR, ndims); idxR[tdir]--;
          eig[count] = VlasovAdvectionCoeff(idxL, dir, solver); count++;
          eig[count] = VlasovAdvectionCoeff(idxR, dir, solver); count++;
          _ArrayCopy1D_(indexL, idxL, ndims); idxL[tdir]++;
          _ArrayCopy1D_(indexR, idxR, ndims); idxR[tdir]++;
          eig[count] = VlasovAdvectionCoeff(idxL, dir, solver); count++;
          eig[count] = VlasovAdvectionCoeff(idxR, dir, solver); count++;
        }
      }
      if (count != neig) {
        fprintf(stderr, "Error in VlasovUpwind(): count != neig for dir=%d\n",dir);
        return 1;
      }

      int all_positive = 1, all_negative = 1;
      double maxabs_eig = 0.0;
      for (int n = 0; n<neig; n++) {
        if (eig[n] <= 0) all_positive = 0;
        if (eig[n] >= 0) all_negative = 0;
        if (absolute(eig[n]) > maxabs_eig) {
          maxabs_eig = absolute(eig[n]);
        }
      }

      if (all_positive) {
        fI[p] = fL[p];
      } else if (all_negative) {
        fI[p] = fR[p];
      } else { 
        fI[p] = 0.5 * (fL[p] + fR[p] - maxabs_eig * (uR[p] - uL[p]));
      }

    }
    _ArrayIncrementIndex_(ndims,bounds_outer,index_outer,done);

  }

  return 0;
}