Euler1DJacobian.c File Reference

Contains the functions compute flux Jacobians for the 1D Euler system. More...

#include <mathfunctions.h>
#include <matmult_native.h>
#include <physicalmodels/euler1d.h>

Go to the source code of this file.

Functions
int	Euler1DJacobian (double *Jac, double *u, void *p, int dir, int nvars, int upw)
int	Euler1DStiffJacobian (double *Jac, double *u, void *p, int dir, int nvars, int upw)

Detailed Description

Contains the functions compute flux Jacobians for the 1D Euler system.

Author

Debojyoti Ghosh

Definition in file Euler1DJacobian.c.

Function Documentation

Euler1DJacobian()

int Euler1DJacobian	(	double *	Jac,
		double *	u,
		void *	p,
		int	dir,
		int	nvars,
		int	upw
	)

Function to compute the flux Jacobian of the 1D Euler equations, given the solution at a grid point. The Jacobian is square matrix of size nvar=3, and is returned as a 1D array (double) of 9 elements in row-major format.

Parameters

Jac	Jacobian matrix: 1D array of size nvar^2 = 9
u	solution at a grid point (array of size nvar = 3)
p	object containing the physics-related parameters
dir	dimension (x/y/z) (not used, since this is 1D system)
nvars	number of vector components
upw	0 -> send back complete Jacobian, 1 -> send back Jacobian of right(+)-moving flux, -1 -> send back Jacobian of left(-)-moving flux

Definition at line 14 of file Euler1DJacobian.c.

{
  Euler1D       *param = (Euler1D*) p;
  static double R[_MODEL_NVARS_*_MODEL_NVARS_], D[_MODEL_NVARS_*_MODEL_NVARS_], 
                L[_MODEL_NVARS_*_MODEL_NVARS_], DL[_MODEL_NVARS_*_MODEL_NVARS_];

  /* get the eigenvalues and left,right eigenvectors */
  _Euler1DEigenvalues_      (u,D,param,0);
  _Euler1DLeftEigenvectors_ (u,L,param,0);
  _Euler1DRightEigenvectors_(u,R,param,0);

  int aupw = absolute(upw), k;
  k = 0; D[k] = absolute( (1-aupw)*D[k] + 0.5*aupw*(1+upw)*max(0,D[k]) + 0.5*aupw*(1-upw)*min(0,D[k]) );
  k = 4; D[k] = absolute( (1-aupw)*D[k] + 0.5*aupw*(1+upw)*max(0,D[k]) + 0.5*aupw*(1-upw)*min(0,D[k]) );
  k = 8; D[k] = absolute( (1-aupw)*D[k] + 0.5*aupw*(1+upw)*max(0,D[k]) + 0.5*aupw*(1-upw)*min(0,D[k]) );

  MatMult3(3,DL,D,L);
  MatMult3(3,Jac,R,DL);

  return(0);
}

Euler1DStiffJacobian()

int Euler1DStiffJacobian	(	double *	Jac,
		double *	u,
		void *	p,
		int	dir,
		int	nvars,
		int	upw
	)

Function to compute the Jacobian of the fast flux (representing the acoustic waves) of the 1D Euler equations, given the solution at a grid point (see _Euler1DSetStiffFlux_, _Euler1DSetStiffJac_). The Jacobian is square matrix of size nvar=3, and is returned as a 1D array (double) of 9 elements in row-major format.

Parameters

Jac	Jacobian matrix: 1D array of size nvar^2 = 9
u	solution at a grid point (array of size nvar = 3)
p	object containing the physics-related parameters
dir	dimension (x/y/z) (not used, since this is 1D system)
nvars	number of vector components
upw	0 -> send back complete Jacobian, 1 -> send back Jacobian of right(+)-moving flux, -1 -> send back Jacobian of left(-)-moving flux

Definition at line 48 of file Euler1DJacobian.c.

{
  Euler1D       *param = (Euler1D*) p;
  static double R[_MODEL_NVARS_*_MODEL_NVARS_], D[_MODEL_NVARS_*_MODEL_NVARS_], 
                L[_MODEL_NVARS_*_MODEL_NVARS_], DL[_MODEL_NVARS_*_MODEL_NVARS_];

  /* get the eigenvalues and left,right eigenvectors */
  _Euler1DEigenvalues_      (u,D,param,0);
  _Euler1DLeftEigenvectors_ (u,L,param,0);
  _Euler1DRightEigenvectors_(u,R,param,0);

  int aupw = absolute(upw), k;
  k = 0; D[k] = 0.0; /* remove the entropy eigenmode */
  k = 4; D[k] = absolute( (1-aupw)*D[k] + 0.5*aupw*(1+upw)*max(0,D[k]) + 0.5*aupw*(1-upw)*min(0,D[k]) );
  k = 8; D[k] = absolute( (1-aupw)*D[k] + 0.5*aupw*(1+upw)*max(0,D[k]) + 0.5*aupw*(1-upw)*min(0,D[k]) );

  MatMult3(3,DL,D,L);
  MatMult3(3,Jac,R,DL);

  return(0);
}