rsolvers/exact.c File Reference

Computes 1D fluxes using exact nonlinear Riemann solver. More...

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Functions
static void	srder (double dm, double vl, double vr, double dmin, double dmax, double *y, double *dydx)
	Equation to solve iteratively for shock and rarefaction as well as its derivative.
static double	rtsafe (void(*funcd)(double, double, double, double, double, double *, double *), double x1, double x2, double xacc, double vl, double vr, double dmin, double dmax)
	Numerical Recipes function rtsafe modified to use doubles and take extra parameters to pass to the derivative function above.
void	fluxes (const Cons1DS Ul, const Cons1DS Ur, const Prim1DS Wl, const Prim1DS Wr, const Real Bxi, Cons1DS *pF)
	Calculates fluxes of CONSERVED variables.
static Real	guessP (const Prim1DS Wl, const Prim1DS Wr)
	Provides a guess value for the pressure in the center region.
static Real	PFunc (const Prim1DS W, Real POld)
	Evaluates the pressure function (see Toro) for the exact riemann solver, given the pressure POld.
static Real	PFuncDeriv (const Prim1DS W, Real POld)
	evaluate the derivative of the pressure function (see Toro) at the pressure value POld
static Real	getPC (const Prim1DS Wl, const Prim1DS Wr)
	Uses Newton-Raphson iteration to find the alebraic root of the pressure function and determine the pressure solution in the center region, Pc.

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Detailed Description

Computes 1D fluxes using exact nonlinear Riemann solver.

PURPOSE: Computes 1D fluxes using exact nonlinear Riemann solver. Currently only isothermal hydrodynamics has been implemented.

REFERENCES:

• R.J. LeVeque, "Numerical Methods for Conservation Laws", 2nd ed., Birkhauser Verlag, Basel, (1992).

• E.F. Toro, "Riemann Solvers and numerical methods for fluid dynamics", 2nd ed., Springer-Verlag, Berlin, (1999).

HISTORY:

• dec-2006 Isothermal hydro version written by Nicole Lemaster
• mar-2010 Adiabatic hydro version 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.c.

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Function Documentation

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

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

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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 482 of file exact.c.

Referenced by integrate_1d_ctu(), integrate_1d_vl(), integrate_2d_ctu(), integrate_2d_vl(), integrate_3d_ctu(), and integrate_3d_vl().

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static Real getPC	(	const Prim1DS	Wl,
		const Prim1DS	Wr
	)			[static]

Uses Newton-Raphson iteration to find the alebraic root of the pressure function and determine the pressure solution in the center region, Pc.

Fails if iteration diverges

Definition at line 433 of file exact.c.

References ath_error(), guessP(), PFunc(), PFuncDeriv(), and Prim1DS::Vx.

Referenced by fluxes().

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static Real guessP	(	const Prim1DS	Wl,
		const Prim1DS	Wr
	)			[static]

Provides a guess value for the pressure in the center region.

The choice is made according to the Two-Shock approximate Riemman solver algorithm. Returns pressure guess value p_0, or TOL if p_0 is less than zero

Definition at line 347 of file exact.c.

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

Referenced by getPC().

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static Real PFunc	(	const Prim1DS	W,
		Real	POld
	)			[static]

Evaluates the pressure function (see Toro) for the exact riemann solver, given the pressure POld.

Definition at line 377 of file exact.c.

References a, Prim1DS::d, f, Gamma, and Prim1DS::P.

Referenced by fluxes(), and getPC().

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static Real PFuncDeriv	(	const Prim1DS	W,
		Real	POld
	)			[static]

evaluate the derivative of the pressure function (see Toro) at the pressure value POld

Definition at line 404 of file exact.c.

References a, Prim1DS::d, Gamma, and Prim1DS::P.

Referenced by getPC().

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static double rtsafe	(	void(*)(double, double, double, double, double, double *, double *)	funcd,
		double	x1,
		double	x2,
		double	xacc,
		double	vl,
		double	vr,
		double	dmin,
		double	dmax
	)			[static]

Numerical Recipes function rtsafe modified to use doubles and take extra parameters to pass to the derivative function above.

Definition at line 284 of file exact.c.

References f.

static void srder	(	double	dm,
		double	vl,
		double	vr,
		double	dmin,
		double	dmax,
		double *	y,
		double *	dydx
	)			[static]

Equation to solve iteratively for shock and rarefaction as well as its derivative.

Used by rtsafe()

Definition at line 266 of file exact.c.