Computes 1D fluxes using exact special relativistic Riemann solver. More...

Enumerations
enum	WaveType { Two_S, RS, SR, Two_R, None }
Functions
void	fluxes (const Cons1DS Ul, const Cons1DS Ur, const Prim1DS Wl, const Prim1DS Wr, const Real Bx, Cons1DS *pF)
	Calculates fluxes of CONSERVED variables.
void	gauleg (double x1, double x2, Real x[], Real w[], int n)
	Given the lower and upper limits of integration x1 and x2, and the abscissas and weights of the Gauss-Legendre n-point quadrature formula.
Real	rtbis_vel (Real(*func)(const Prim1DS Wl, const Prim1DS Wr, Real p), const Prim1DS Wl, const Prim1DS Wr, Real x1, Real x2, Real xacc)
	Implements bisection root finding algorithm to solve the velocity eqn.
Real	getDelVRel (const Prim1DS Wl, const Prim1DS Wr, Real p)
	Determine vRel for the wave pattern indicated by wave.
Real	getVRel_2R (const Prim1DS Wl, const Prim1DS Wr, Real p)
	Determine vRel for the case of two rarefactions.
Real	getVRel_RS (const Prim1DS Wl, const Prim1DS Wr, Real p)
	Determine vRel for the case of rarefaction-shock wave.
Real	getVRel_2S (const Prim1DS Wl, const Prim1DS Wr, Real p)
	Determine vRel for the case of two shocks.
Real	getVlim_2S (const Prim1DS Wl, const Prim1DS Wr)
	Determine vlim for the case of two shocks (eq 4.5).
Real	getVlim_RS (const Prim1DS Wl, const Prim1DS Wr)
	Determine vlim for the case of rarefaction-shock (eq 4.10).
Real	getVlim_2R (const Prim1DS Wl, const Prim1DS Wr)
	Determine vlim for two rarefactions (eq.
Real	integrateRaref (const Prim1DS W, Real a, Real b)
	Numerically integrate the integral for rarefactions (eq 3.22 in RZP) using Gaussian-Legendre quadrature.
Real	getP (const Prim1DS Wl, const Prim1DS Wr)
	Determine the pressure in the intermediate state using interval bisection.
void	getShockVars (const Prim1DS Wa, Real Pb, char dir, Real pJ, Real pV_shock, Real *pd)
	Determine the mass flux, shock velocity and density across a shock wave.
Real	getVb_Shock (const Prim1DS Wa, Real Pb, char dir)
	Determine the normal velocity behind a shock wave.
Real	getVb_Raref (const Prim1DS Wa, Real Pb, char dir)
	Determine the normal velocity behind a rarefaction wave.
Real	getXi (const Prim1DS Wa, Real P, Real vxc, char dir)
	Determine the self-similarity variable xi for rarefactions (eq 3.15).
Real	rtbis_xi (Real(*func)(const Prim1DS Wa, Real P, Real vx, char), const Prim1DS Wa, char dir, Real f_x1, Real f_x2, Real x1, Real x2, Real xacc)
	Implements bisection root finding algorithm to find the rarefaction head and tail velocity.
void	getVelT_Raref (const Prim1DS Wa, Real P, Real vxb, Real pVy, Real pVz)
	Determine the tangential velocities vy and vz behind a rarefaction wave.
void	getVelT_Shock (const Prim1DS Wa, Real P, Real vxb, Real pVy, Real pVz)
	Determine the tangential velocitiies vy and vz behind a shock wave.
void	setFluxes (Real vx, Real vy, Real vz, Real P, Real d, Cons1DS *pF)
	Set the corresponding fluxes as the fields of pF.
Variables
static enum WaveType	wave

Detailed Description

Computes 1D fluxes using exact special relativistic Riemann solver.

PURPOSE: Computes 1D fluxes using exact special relativistic Riemann solver. currently works only for hydrodynamics

REFERENCES:

Rezzolla, Zanotti, and Pons. "An Improved Exact Riemann Solver for Multidimensional Relativistic Flows." 2002.

HISTORY:

April-2010: Written by Nick Hand.

CONTAINS PUBLIC FUNCTIONS:

fluxes() - all Riemann solvers in Athena must have this function name and use the same argument list as defined in rsolvers/prototypes.h ============================================================================

Definition in file exact_sr.c.

Enumeration Type Documentation

enum WaveType

Enumerator:

Two_S
RS
SR
Two_R
None

Definition at line 44 of file exact_sr.c.

Function Documentation

void fluxes	(	const Cons1DS	Ul,
		const Cons1DS	Ur,
		const Prim1DS	Wl,
		const Prim1DS	Wr,
		const Real	Bx,
		Cons1DS *	pF
	)

Calculates fluxes of CONSERVED variables.

Computes 1D fluxes Input Arguments:

Bxi = B in direction of slice at cell interface
Ul,Ur = L/R-states of CONSERVED variables at cell interface Output Arguments:
pFlux = pointer to fluxes of CONSERVED variables at cell interface.

Computes 1D fluxes.

Compute 1D fluxes Input Arguments:

Bxi = B in direction of slice at cell interface
Ul,Ur = L/R-states of CONSERVED variables at cell interface.

Computes 1D fluxes Input Arguments:

Ul,Ur = L/R-states of CONSERVED variables at cell interface
Wl,Wr = L/R-states of PRIMITIVE variables at cell interface Output Arguments:
pFlux = pointer to fluxes of CONSERVED variables at cell interface.

Computes 1D fluxes Input Arguments:

Ul,Ur = L/R-states of CONSERVED variables at cell interface Output Arguments:
pFlux = pointer to fluxes of CONSERVED variables at cell interface.

Computes 1D fluxes Input Arguments:

Bxi = B in direction of 1D slice at cell interface
Ul,Ur = L/R-states of CONSERVED variables at cell interface Output Arguments:
pFlux = pointer to fluxes of CONSERVED variables at cell interface.

Computes 1D fluxes using exact special relativistic Riemann solver.

Computes fluxes of CONSERVES variables.

Input Arguments:

Bxi = B in direction of slice at cell interface
Ul,Ur = L/R-states of CONSERVED variables at cell interface Output Arguments:
pFlux = pointer to fluxes of CONSERVED variables at cell interface

Input Arguments:

Bxi = B in direction of slice at cell interface
Ul,Ur = L/R-states of CONSERVED variables at cell interface Output Arguments:
pF = pointer to fluxes of CONSERVED variables at cell interface

Input Arguments:

Ul,Ur = L/R-states of CONSERVED variables at cell interface
Bx = B in direction of slice at cell interface Output Arguments:
pF = pointer to fluxes of CONSERVED variables at cell interface

--------------------------------------------------------------------------

Output Arguments:

Flux = fluxes of CONSERVED variables at cell interface

Input Arguments:

Ul,Ur = L/R-states of CONSERVED variables at cell interface
Bx = B in direction of slice at cell interface Output Arguments:
pFlux = pointer to fluxes of CONSERVED variables at cell interface

Definition at line 103 of file exact_sr.c.

References C, Prim1DS::d, Gamma, getP(), getShockVars(), getVb_Raref(), getVb_Shock(), getVelT_Raref(), getVelT_Shock(), getXi(), Prim1DS::P, RS, rtbis_xi(), setFluxes(), SR, Two_R, Two_S, Prim1DS::Vx, Prim1DS::Vy, Prim1DS::Vz, vz, and wave.

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void gauleg	(	double	x1,
		double	x2,
		Real	x[],
		Real	w[],
		int	n
	)

Given the lower and upper limits of integration x1 and x2, and the abscissas and weights of the Gauss-Legendre n-point quadrature formula.

Given the lower and upper limits of integration x1 and x2, and given n, this routine returns arrays x[1..n] and w[1..n] of length n, containing the abscissas and weights of the Gauss-Legendre n-point quadrature formula. See Numerical Recipes in C, Press et al.

Definition at line 826 of file exact_sr.c.

Referenced by integrateRaref().

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Real getDelVRel	(	const Prim1DS	Wl,
		const Prim1DS	Wr,
		Real	p
	)

Determine vRel for the wave pattern indicated by wave.

Definition at line 467 of file exact_sr.c.

References getVRel_2R(), getVRel_2S(), getVRel_RS(), RS, SR, Two_R, Two_S, Prim1DS::Vx, and wave.

Referenced by getP().

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Real getP	(	const Prim1DS	Wl,
		const Prim1DS	Wr
	)

Determine the pressure in the intermediate state using interval bisection.

Definition at line 492 of file exact_sr.c.

References getDelVRel(), getVlim_2S(), getVlim_RS(), Prim1DS::P, rtbis_vel(), tol, Prim1DS::Vx, and wave.

Referenced by fluxes().

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void getShockVars	(	const Prim1DS	Wa,
		Real	Pb,
		char	dir,
		Real *	pJ,
		Real *	pV_shock,
		Real *	pd
	)

Determine the mass flux, shock velocity and density across a shock wave.

Definition at line 336 of file exact_sr.c.

References ath_error(), C, Prim1DS::d, Gamma, J, Prim1DS::P, Prim1DS::Vx, Prim1DS::Vy, and Prim1DS::Vz.

Referenced by fluxes(), and getVb_Shock().

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Real getVb_Raref	(	const Prim1DS	Wa,
		Real	Pb,
		char	dir
	)

Determine the normal velocity behind a rarefaction wave.

Definition at line 655 of file exact_sr.c.

References integrateRaref(), Prim1DS::P, and Prim1DS::Vx.

Referenced by fluxes(), getVlim_2R(), getVlim_RS(), getVRel_2R(), getVRel_RS(), and rtbis_xi().

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Real getVb_Shock	(	const Prim1DS	Wa,
		Real	Pb,
		char	dir
	)

Determine the normal velocity behind a shock wave.

Definition at line 632 of file exact_sr.c.

References Prim1DS::d, Gamma, getShockVars(), J, Prim1DS::P, Prim1DS::Vx, Prim1DS::Vy, and Prim1DS::Vz.

Referenced by fluxes(), getVlim_2S(), getVRel_2S(), and getVRel_RS().

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void getVelT_Raref	(	const Prim1DS	Wa,
		Real	P,
		Real	vxb,
		Real *	pVy,
		Real *	pVz
	)

Determine the tangential velocities vy and vz behind a rarefaction wave.

Definition at line 702 of file exact_sr.c.

References C, Prim1DS::d, Gamma, Prim1DS::P, Prim1DS::Vx, Prim1DS::Vy, and Prim1DS::Vz.

Referenced by fluxes().

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void getVelT_Shock	(	const Prim1DS	Wa,
		Real	P,
		Real	vxb,
		Real *	pVy,
		Real *	pVz
	)

Determine the tangential velocitiies vy and vz behind a shock wave.

Note that this function differs from Pons et al. (2000) equation 4.13, which is only valid for one of vz or vy equal to zero.

Definition at line 753 of file exact_sr.c.

References Prim1DS::d, Gamma, Prim1DS::P, Prim1DS::Vx, Prim1DS::Vy, Prim1DS::Vz, and vz.

Referenced by fluxes().

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Real getVlim_2R	(	const Prim1DS	Wl,
		const Prim1DS	Wr
	)

Determine vlim for two rarefactions (eq.

4.12 in RZP)

Definition at line 393 of file exact_sr.c.

References getVb_Raref(), and Prim1DS::Vx.

Referenced by rtbis_vel().

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Real getVlim_2S	(	const Prim1DS	Wl,
		const Prim1DS	Wr
	)

Determine vlim for the case of two shocks (eq 4.5).

Definition at line 443 of file exact_sr.c.

References getVb_Shock(), Prim1DS::P, and Prim1DS::Vx.

Referenced by getP(), and rtbis_vel().

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Real getVlim_RS	(	const Prim1DS	Wl,
		const Prim1DS	Wr
	)

Determine vlim for the case of rarefaction-shock (eq 4.10).

Definition at line 415 of file exact_sr.c.

References a, getVb_Raref(), Prim1DS::P, and Prim1DS::Vx.

Referenced by getP(), and rtbis_vel().

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Real getVRel_2R	(	const Prim1DS	Wl,
		const Prim1DS	Wr,
		Real	p
	)

Determine vRel for the case of two rarefactions.

Definition at line 548 of file exact_sr.c.

References getVb_Raref(), and Prim1DS::Vx.

Referenced by getDelVRel().

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Real getVRel_2S	(	const Prim1DS	Wl,
		const Prim1DS	Wr,
		Real	p
	)

Determine vRel for the case of two shocks.

Definition at line 609 of file exact_sr.c.

References ath_3d_fft_plan::dir, getVb_Shock(), J, and Prim1DS::Vx.

Referenced by getDelVRel().

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Real getVRel_RS	(	const Prim1DS	Wl,
		const Prim1DS	Wr,
		Real	p
	)

Determine vRel for the case of rarefaction-shock wave.

Definition at line 570 of file exact_sr.c.

References getVb_Raref(), getVb_Shock(), J, SR, Prim1DS::Vx, and wave.

Referenced by getDelVRel().

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Real getXi	(	const Prim1DS	Wa,
		Real	P,
		Real	vxc,
		char	dir
	)

Determine the self-similarity variable xi for rarefactions (eq 3.15).

Definition at line 671 of file exact_sr.c.

References Prim1DS::d, Gamma, Prim1DS::P, Prim1DS::Vx, Prim1DS::Vy, and Prim1DS::Vz.

Referenced by fluxes().

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Real integrateRaref	(	const Prim1DS	W,
		Real	a,
		Real	b
	)

Numerically integrate the integral for rarefactions (eq 3.22 in RZP) using Gaussian-Legendre quadrature.

Definition at line 284 of file exact_sr.c.

References Prim1DS::d, f, Gamma, gauleg(), n, Prim1DS::P, Prim1DS::Vx, Prim1DS::Vy, and Prim1DS::Vz.

Referenced by getVb_Raref().

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Real rtbis_vel	(	Real(*)(const Prim1DS Wl, const Prim1DS Wr, Real p)	func,
		const Prim1DS	Wl,
		const Prim1DS	Wr,
		Real	x1,
		Real	x2,
		Real	xacc
	)

Implements bisection root finding algorithm to solve the velocity eqn.

Assumes func(x1) and func(x2) have opposite signs without a check

Definition at line 868 of file exact_sr.c.

References f, getVlim_2R(), getVlim_2S(), getVlim_RS(), RS, SR, Two_R, Two_S, Prim1DS::Vx, and wave.

Referenced by getP().

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Real rtbis_xi	(	Real(*)(const Prim1DS Wa, Real P, Real vx, char)	func,
		const Prim1DS	Wa,
		char	dir,
		Real	f_x1,
		Real	f_x2,
		Real	x1,
		Real	x2,
		Real	xacc
	)

Implements bisection root finding algorithm to find the rarefaction head and tail velocity.

Assumes func(x1) and func(x2) have opposite signs without a check

Definition at line 916 of file exact_sr.c.

References f, and getVb_Raref().

Referenced by fluxes().

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void setFluxes	(	Real	vx,
		Real	vy,
		Real	vz,
		Real	P,
		Real	d,
		Cons1DS *	pF
	)

Set the corresponding fluxes as the fields of pF.

Definition at line 796 of file exact_sr.c.

References ath_error(), Cons1DS::d, Cons1DS::E, Gamma, Cons1DS::Mx, Cons1DS::My, and Cons1DS::Mz.

Referenced by fluxes().

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Variable Documentation

enum WaveType wave [static]

Definition at line 46 of file exact_sr.c.

Referenced by fluxes(), getDelVRel(), getP(), getVRel_RS(), and rtbis_vel().

rsolvers/exact_sr.c File Reference

Enumerations

Functions

Variables

Detailed Description

Enumeration Type Documentation

Function Documentation

Variable Documentation