glm.c File Reference

GLM module implementation. More...

#include "pluto.h"

Functions
void	GLM_Solve (const State_1D *state, double **VL, double **VR, int beg, int end, Grid *grid)
void	GLM_Source (const Data_Arr Q, double dt, Grid *grid)
void	EGLM_Source (const State_1D *state, double dt, int beg, int end, Grid *grid)
void	GLM_Init (const Data *d, const Time_Step *Dts, Grid *grid)

Variables
double	glm_ch = -1.0

Detailed Description

Contains functions for the GLM module.

Authors

A. Mignone (migno.nosp@m.ne@p.nosp@m.h.uni.nosp@m.to.i.nosp@m.t)
P. Tzeferacos (petro.nosp@m.s.tz.nosp@m.efera.nosp@m.cos@.nosp@m.ph.un.nosp@m.ito..nosp@m.it)

Date

Aug 16, 2012

Function Documentation

void EGLM_Source	(	const State_1D *	state,
		double	dt,
		int	beg,
		int	end,
		Grid *	grid
	)

Add source terms to the right hand side of the conservative equations, momentum and energy equations only. This yields the extended GLM (EGLM) given by Eq. (24a)–(24c) in

"Hyperbolic Divergence cleaning for the MHD Equations" Dedner et al. (2002), JcP, 175, 645

void GLM_Init	(	const Data *	d,
		const Time_Step *	Dts,
		Grid *	grid
	)

Initialize the maximum propagation speed glm_ch.

void GLM_Solve	(	const State_1D *	state,
		double **	VL,
		double **	VR,
		int	beg,
		int	end,
		Grid *	grid
	)

Solve the 2x2 linear hyperbolic GLM-MHD system given by the divergence cleaning approach. Build new states VL and VR for Riemann problem. We use Eq. (42) of

Dedner et al. "Hyperbolic Divergence Cleaning for the MHD equations", JCP 175, 645 (2002)

Parameters

[in,out]	state	pointer to a State_1D structure
[out]	VL	left-interface state to be passed to the Riemann solver
[out]	VR	right-interface state to be passed to the Riemann solver
[in]	beg	starting index of computation
[in]	end	final index of computation
[in]	grid	pointer to array of Grid structures

The purpose of this function is two-fold:

1. assign a unique value to the normal component of magnetic field and to te scalar psi before the actual Riemann solver is called.
2. compute GLM fluxes in Bn and psi.

The following MAPLE script has been used

restart;
with(linalg);
A := matrix(2,2,[ 0, 1, c^2, 0]);

R := matrix(2,2,[ 1, 1, c, -c]);
L := inverse(R);
E := matrix(2,2,[c,0,0,-c]);
multiply(R,multiply(E,L));

void GLM_Source	(	const Data_Arr	Q,
		double	dt,
		Grid *	grid
	)

Include the parabolic source term of the Lagrangian multiplier equation in a split fashion for the mixed GLM formulation. Ref. Mignone & Tzeferacos, JCP (2010) 229, 2117, Equation (27).

Variable Documentation

double glm_ch = -1.0

The propagation speed of divergence error.