glm.h File Reference

Header file for GLM Divergence Cleaning. More...

Go to the source code of this file.

Macros
#define	EGLM   NO

Functions
void	GLM_Solve (const State_1D *, double **, double **, int, int, Grid *)
void	GLM_Init (const Data *, const Time_Step *, Grid *)
void	GLM_Source (const Data_Arr, double, Grid *)
void	EGLM_Source (const State_1D *, double, int, int, Grid *)

Variables
double	glm_ch

Detailed Description

Contains function prototypes and global variable declaration for the GLM formulation to control the divergence-free condition of magnetic field.

References

• "A Second-order unsplit Godunov scheme for cell-centered MHD: The CTU-GLM scheme"
  Mignone & Tzeferacos, JCP (2010) 229, 2117

• "High-order conservative finite difference GLM-MHD scheme for cell-centered MHD"
  Mignone, Tzeferacos & Bodo, JCP (2010) 229, 5896

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

Sep 28, 2012

Macro Definition Documentation

#define EGLM   NO

The EGLM macro may be turned to YES to enable the extended GLM formalism. Although it breaks conservation of momentum and energy, it has proven to be more robust in treating low-beta plasma.

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

The propagation speed of divergence error.