Functions to evaluate the eigenvalues, and left- and right-eigenvectors of "Roe's matrix A" for the linearized system in the CONSERVED variables. More...

Functions
void	esys_roe_iso_hyd (const Real v1, const Real v2, const Real v3, Real eigenvalues[], Real right_eigenmatrix[][4], Real left_eigenmatrix[][4])
	ISOTHERMAL HYDRO.
void	esys_roe_adb_hyd (const Real v1, const Real v2, const Real v3, const Real h, Real eigenvalues[], Real right_eigenmatrix[][5], Real left_eigenmatrix[][5])
void	esys_roe_iso_mhd (const Real d, const Real v1, const Real v2, const Real v3, const Real b1, const Real b2, const Real b3, const Real x, const Real y, Real eigenvalues[], Real right_eigenmatrix[][6], Real left_eigenmatrix[][6])
	ISOTHERMAL MHD.
void	esys_roe_adb_mhd (const Real d, const Real v1, const Real v2, const Real v3, const Real h, const Real b1, const Real b2, const Real b3, const Real x, const Real y, Real eigenvalues[], Real right_eigenmatrix[][7], Real left_eigenmatrix[][7])

Detailed Description

Functions to evaluate the eigenvalues, and left- and right-eigenvectors of "Roe's matrix A" for the linearized system in the CONSERVED variables.

PURPOSE: Functions to evaluate the eigenvalues, and left- and right-eigenvectors of "Roe's matrix A" for the linearized system in the CONSERVED variables, i.e. U,t = AU,x, where U=(d,d*vx,d*vy,d*vz,[E],[By,Bz]). The eigenvalues are returned through the argument list as a vector of length NWAVE. The eigenvectors are returned as matrices of size (NWAVE)x(NWAVE), with right-eigenvectors stored as COLUMNS (so R_i = right_eigenmatrix[*][i]), and left-eigenvectors stored as ROWS (so L_i = left_eigenmatrix[i][*]).

To improve performance components of the eigenvectors which are zero are not set here (eigenmatrices must be initialized to zero in calling routine). However, for completeness, statements which set these values are included but are commented out.

If the input argument for the left- or right-eigenmatrix is set to the NULL pointer, only the eigenvalues are returned

The "Roe-averaging" of the L/R states must be performed in the calling funct

REFERENCES:

P. Cargo & G. Gallice, "Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws", JCP, 136, 446 (1997)

J. Stone, T. Gardiner, P. Teuben, J. Hawley, & J. Simon "Athena: A new code for astrophysical MHD", ApJS, (2008), Appendix B Equation numbers refer to this paper.

CONTAINS PUBLIC FUNCTIONS:

Definition in file esystem_roe.c.

Function Documentation

void esys_roe_adb_hyd	(	const Real	v1,
		const Real	v2,
		const Real	v3,
		const Real	h,
		Real	eigenvalues[],
		Real	right_eigenmatrix[][5],
		Real	left_eigenmatrix[][5]
	)

Definition at line 132 of file esystem_roe.c.

References a, and Gamma_1.

Referenced by fluxes(), HLLE_FUNCTION(), and problem().

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void esys_roe_adb_mhd	(	const Real	d,
		const Real	v1,
		const Real	v2,
		const Real	v3,
		const Real	h,
		const Real	b1,
		const Real	b2,
		const Real	b3,
		const Real	x,
		const Real	y,
		Real	eigenvalues[],
		Real	right_eigenmatrix[][7],
		Real	left_eigenmatrix[][7]
	)

Definition at line 432 of file esystem_roe.c.

References Gamma_1, Gamma_2, and s.

Referenced by fluxes(), HLLE_FUNCTION(), and problem().

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void esys_roe_iso_hyd	(	const Real	v1,
		const Real	v2,
		const Real	v3,
		Real	eigenvalues[],
		Real	right_eigenmatrix[][4],
		Real	left_eigenmatrix[][4]
	)

ISOTHERMAL HYDRO.

Input: v1,v2,v3 = Roe averaged components of velocity
Output: eigenvalues[4],right_eigenmatrix[4,4],left_eigenmatrix[4,4]

Definition at line 62 of file esystem_roe.c.

References Iso_csound.

Referenced by fluxes(), HLLE_FUNCTION(), and problem().

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void esys_roe_iso_mhd	(	const Real	d,
		const Real	v1,
		const Real	v2,
		const Real	v3,
		const Real	b1,
		const Real	b2,
		const Real	b3,
		const Real	x,
		const Real	y,
		Real	eigenvalues[],
		Real	right_eigenmatrix[][6],
		Real	left_eigenmatrix[][6]
	)

ISOTHERMAL MHD.

Input: d,v1,v2,v3,b1,b2,b3 = Roe averaged density, velocities, and B field x,y = numerical factors (eqs. )
Output: eigenvalues[6], right_eigenmatrix[6,6], left_eigenmatrix[6,6];

Definition at line 232 of file esystem_roe.c.

References Iso_csound2, and s.

Referenced by fluxes(), HLLE_FUNCTION(), and problem().

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rsolvers/esystem_roe.c File Reference

Functions

Detailed Description

Function Documentation