GodunovUtilities Class Reference

#include <GodunovUtilities.H>

Detailed Description

Utility class for higher-order Godunov methods: slopes, parabolic interpolants, limiters. Contains no physics-dependent methods, but one of the member functions (PPMFaceValues()) may require a pointer to a GodunovPhysics class in order to set boundary slopes.


Public Member Functions
	GodunovUtilities ()
	Constructor.
	~GodunovUtilities ()
	Destructor.
void	define (const ProblemDomain &a_domain, const Real &a_dx)
	Define the object.
Slopes
void	vanLeerSlopes (FArrayBox &a_dW, const FArrayBox &a_W, const int &a_numSlopes, const bool &a_useLimiting, const int &a_dir, const Box &a_box)
	Compute componentwise van Leer slopes.
void	fourthOrderSlopes (FArrayBox &a_dW4, const FArrayBox &a_W, const FArrayBox &a_dWvL, const int &a_numSlopes, const int &a_dir, const Box &a_box)
	Compute fourth-order slopes.
void	oneSidedDifferences (FArrayBox &a_dWMinus, FArrayBox &a_dWPlus, const FArrayBox &a_W, const int &a_dir, const Box &a_box)
	Compute slopes (dW- and dW+) using one sided differences.
void	slopes (FArrayBox &a_dWCent, FArrayBox &a_dWMinus, FArrayBox &a_dWPlus, const FArrayBox &a_W, const int &a_numSlopes, const int &a_dir, const Box &a_loBox, const Box &a_hiBox, const Box &a_centerBox, const Box &a_entireBox, const int &a_hasLo, const int &a_hasHi)
	Compute slopes (dW (center), dW-, and dW+).
Parabolic interpolants
void	PLMNormalPred (FArrayBox &a_dWCharMinus, FArrayBox &a_dWCharPlus, const FArrayBox &a_dWChar, const FArrayBox &a_Lambda, const Real &a_dtbydx, const Box &a_box)
	PLM normal predictor.
void	PPMFaceValues (FArrayBox &a_WFace, const FArrayBox &a_W, const int &a_numSlopes, const bool &a_useLimiting, const int &a_dir, const Box &a_box, const Real &a_time, const GodunovPhysics *a_physPtr=NULL)
	PPM face-centered interpolant.
void	PPMNormalPred (FArrayBox &a_dWMinus, FArrayBox &a_dWPlus, const FArrayBox &a_Lambda, const Real &a_dtbydx, const int &a_numSlopes, const Box &a_box)
	PPM normal predictor.
Limiters
void	slopeLimiter (FArrayBox &a_dW, const FArrayBox &a_dWMinus, const FArrayBox &a_dWPlus, const int &a_numSlopes, const Box &a_box)
	van Leer slope limiter.
void	slopeLimiterExtPreserving (FArrayBox &a_dW, const FArrayBox &a_dWMinus, const FArrayBox &a_dWPlus, const int &a_numSlopes, const Box &a_box, const int &a_dir)
	extremum-preserving van Leer slope limiter.
void	PPMLimiter (FArrayBox &a_dWMinus, FArrayBox &a_dWPlus, const FArrayBox &a_W, const int &a_numSlopes, const int &a_dir, const Box &a_box)
	PPM Limiter.
void	highOrderLimiter (bool a_highOrderLimiter)
	Set whether to use high-order limiter.
bool	useHighOrderLimiter () const
	query whether we're using the high-order limiter
Dissipation mechanisms
void	computeFlattening (FArrayBox &a_flattening, const FArrayBox &a_W, const Interval &a_velInt, const int &a_presInd, const Real &a_smallPres, const int &a_bulkModulusInd, const Box &a_box)
	Compute the slope flattening coefficients.
void	applyFlattening (FArrayBox &a_dW, const FArrayBox &a_flat, const Box &a_box)
	Apply the flattening to slopes.
void	artificialViscosity (FArrayBox &a_F, const FArrayBox &a_U, const FArrayBox &a_divVel, const Real &a_scale, const int &a_dir, const Box &a_box)
	Compute face-centered artificial viscosity flux.
Divergence
void	divVel (FArrayBox &a_divVel, const FArrayBox &a_W, const Interval &a_velInt, const int &a_dir, const Box &a_box)
	Compute face-centered velocity divergence.
void	divVelHO (FArrayBox &a_divVel, const FArrayBox &a_W, const int &a_dir, const Box &a_box, GodunovPhysics *a_physPtr)
	Compute high-order face-centered velocity divergence for artificial viscosity.
Deconvolution and convolution
void	deconvolve (FArrayBox &a_avgFab, const FArrayBox &a_cellFab, int a_sign=1)
	Deconvolve from cell-centered to cell-averaged data (or vice versa).
void	deconvolve (FArrayBox &a_avgFab, const FArrayBox &a_cellFab, const Box &a_box, int a_sign=1)
	Deconvolve from cell-centered to cell-averaged data (or vice versa) on a specified box.
void	deconvolveFace (FluxBox &a_avgFlux, const FluxBox &a_cellFlux, int a_sign=1)
	Deconvolve from face-centered to face-averaged data (or vice versa).
void	deconvolveFace (FluxBox &a_avgFlux, const FluxBox &a_cellFlux, const Box &a_box, int a_sign=1)
	Deconvolve from face-centered to face-averaged data (or vice versa) on a specified box.
Protected Attributes
ProblemDomain	m_domain
Real	m_dx
bool	m_isDefined
bool	m_highOrderLimiter
Private Member Functions
void	operator= (const GodunovUtilities &)
	GodunovUtilities (const GodunovUtilities &)

Constructor & Destructor Documentation

GodunovUtilities::GodunovUtilities ( )

Constructor.

GodunovUtilities::~GodunovUtilities ( )

Destructor.

GodunovUtilities::GodunovUtilities ( const GodunovUtilities & ) [private]

Member Function Documentation

void GodunovUtilities::define	(	const ProblemDomain &	a_domain,
		const Real &	a_dx
	)

Define the object.

void GodunovUtilities::vanLeerSlopes	(	FArrayBox &	a_dW,
		const FArrayBox &	a_W,
		const int &	a_numSlopes,
		const bool &	a_useLimiting,
		const int &	a_dir,
		const Box &	a_box
	)

Compute componentwise van Leer slopes.

Given cell averages W, compute van Leer slopes dW on a component-by-component basis.

void GodunovUtilities::fourthOrderSlopes	(	FArrayBox &	a_dW4,
		const FArrayBox &	a_W,
		const FArrayBox &	a_dWvL,
		const int &	a_numSlopes,
		const int &	a_dir,
		const Box &	a_box
	)

Compute fourth-order slopes.

Given cell averages W and van Leer slopes dWvL, compute fourth-order slopes dW4. Limiting is performed in a separate pass.

void GodunovUtilities::oneSidedDifferences	(	FArrayBox &	a_dWMinus,
		FArrayBox &	a_dWPlus,
		const FArrayBox &	a_W,
		const int &	a_dir,
		const Box &	a_box
	)

Compute slopes (dW- and dW+) using one sided differences.

void GodunovUtilities::slopes	(	FArrayBox &	a_dWCent,
		FArrayBox &	a_dWMinus,
		FArrayBox &	a_dWPlus,
		const FArrayBox &	a_W,
		const int &	a_numSlopes,
		const int &	a_dir,
		const Box &	a_loBox,
		const Box &	a_hiBox,
		const Box &	a_centerBox,
		const Box &	a_entireBox,
		const int &	a_hasLo,
		const int &	a_hasHi
	)

Compute slopes (dW (center), dW-, and dW+).

a_dwCent, a_dwMinus, a_dWPlus, and a_dW all live on cell-centered a_entireBox.

For i in a_centerBox: a_dwCent[i] = (a_W[i+1] - a_W[i-1])/2; a_dWMinus[i] = a_W[i] - a_W[i-1]; a_dWPlus[i] = a_W[i+1] - a_W[i].

For i in a_loBox, set only a_dWPlus[i] = a_W[i+1] - a_W[i] and copy it to a_dWCent[i] and a_dWMinus[i].

For i in a_hiBox, set only a_dWMinus[i] = a_W[i] - a_W[i-1] and copy it to a_dWCent[i] and a_dWPlus[i].

void GodunovUtilities::PLMNormalPred	(	FArrayBox &	a_dWCharMinus,
		FArrayBox &	a_dWCharPlus,
		const FArrayBox &	a_dWChar,
		const FArrayBox &	a_Lambda,
		const Real &	a_dtbydx,
		const Box &	a_box
	)

PLM normal predictor.

Compute the increments in the characteristic amplitudes.

void GodunovUtilities::PPMFaceValues	(	FArrayBox &	a_WFace,
		const FArrayBox &	a_W,
		const int &	a_numSlopes,
		const bool &	a_useLimiting,
		const int &	a_dir,
		const Box &	a_box,
		const Real &	a_time,
		const GodunovPhysics *	a_physPtr = `NULL`
	)

PPM face-centered interpolant.

Given the cell average a_W, compute fourth-order accurate face-centered values WFace on a_box by differentiating the indefinite integral. Limiting is performed in a separate pass.

void GodunovUtilities::PPMNormalPred	(	FArrayBox &	a_dWMinus,
		FArrayBox &	a_dWPlus,
		const FArrayBox &	a_Lambda,
		const Real &	a_dtbydx,
		const int &	a_numSlopes,
		const Box &	a_box
	)

PPM normal predictor.

On input, dW(Minus,Plus), contain the characteristic expansions of the differences between the (minus, plus) face values and the cell average. On output, dW(Minus,Plus) contain the characteristic amplitudes of the corrections required to compute the normal predictor.

void GodunovUtilities::slopeLimiter	(	FArrayBox &	a_dW,
		const FArrayBox &	a_dWMinus,
		const FArrayBox &	a_dWPlus,
		const int &	a_numSlopes,
		const Box &	a_box
	)

van Leer slope limiter.

On input, dW contains the centered, unlimited slopes, and dW(Minus,Plus) contain the one-sided slopes from the minus, plus sides. On output, dW contains the limited slopes. slopes dW4. Limiting is performed in a separate pass.

void GodunovUtilities::slopeLimiterExtPreserving	(	FArrayBox &	a_dW,
		const FArrayBox &	a_dWMinus,
		const FArrayBox &	a_dWPlus,
		const int &	a_numSlopes,
		const Box &	a_box,
		const int &	a_dir
	)

extremum-preserving van Leer slope limiter.

On input, dW contains the centered, unlimited slopes, and dW(Minus,Plus) contain the one-sided slopes from the minus, plus sides. On output, dW contains the limited slopes. slopes dW4. Limiting is performed in a separate pass.

void GodunovUtilities::PPMLimiter	(	FArrayBox &	a_dWMinus,
		FArrayBox &	a_dWPlus,
		const FArrayBox &	a_W,
		const int &	a_numSlopes,
		const int &	a_dir,
		const Box &	a_box
	)

PPM Limiter.

a_dWMinus and a_dWPlus are the differences between the face values on the minus and plus sides of cells and the average in the cell. That is, a_dWMinus[i] = WFace[i - e/2] - a_W[i] a_dWPlus[i] = WFace[i + e/2] - a_W[i] where e is the unit vector in dimension a_dir. The PPM limiter is applied to these values to obtain a monotone interpolant in the cell. The function returns the limited a_dWMinus and a_dWPlus on a_box. petermc, 4 Sep 2008: included a_W in argument list

If m_highOrderLimiter, then need a_dWMinus and a_dWPlus on a_box, and need a_W on on a_box grown by 3 in dimension a_dir. Returns limited a_dWMinus and a_dWPlus on a_box.

void GodunovUtilities::highOrderLimiter ( bool a_highOrderLimiter )

Set whether to use high-order limiter.

bool GodunovUtilities::useHighOrderLimiter ( ) const [inline]

query whether we're using the high-order limiter

References m_highOrderLimiter.

void GodunovUtilities::computeFlattening	(	FArrayBox &	a_flattening,
		const FArrayBox &	a_W,
		const Interval &	a_velInt,
		const int &	a_presInd,
		const Real &	a_smallPres,
		const int &	a_bulkModulusInd,
		const Box &	a_box
	)

Compute the slope flattening coefficients.

Compute the slope flattening coefficients, a_flattening, using the primitive variables, a_W, within a_box.

Parameters:

a_flattening	flattening coeffs, 1 component on a_box
a_W	primitive variables, on a_box grown by 3 within m_domain
a_velInt	interval of a_W with velocity; length SpaceDim
a_presInd	index of a_W with pressure
a_smallPres	minimum pressure to use in ratio
a_bulkModulusInd	index of a_W with bulk modulus
a_box	cell-centered box on which a_flattening lives

void GodunovUtilities::applyFlattening	(	FArrayBox &	a_dW,
		const FArrayBox &	a_flat,
		const Box &	a_box
	)

Apply the flattening to slopes.

Multiply every component of a_dW by a_flat, on a_box.

Parameters:

a_dW	slopes to be flattened, on at least a_box
a_flat	cell-centered flattening coefficients, on at least a_box
a_box	cell-centered box on which to flatten

void GodunovUtilities::artificialViscosity	(	FArrayBox &	a_F,
		const FArrayBox &	a_U,
		const FArrayBox &	a_divVel,
		const Real &	a_scale,
		const int &	a_dir,
		const Box &	a_box
	)

Compute face-centered artificial viscosity flux.

Increments face-centered flux in the a_dir direction with quadratic artificial viscosity.

void GodunovUtilities::divVel	(	FArrayBox &	a_divVel,
		const FArrayBox &	a_W,
		const Interval &	a_velInt,
		const int &	a_dir,
		const Box &	a_box
	)

Compute face-centered velocity divergence.

Returns face-centered velocity divergence on faces in the direction a_dir. The velocities are the components a_velInterval of a_W.

void GodunovUtilities::divVelHO	(	FArrayBox &	a_divVel,
		const FArrayBox &	a_W,
		const int &	a_dir,
		const Box &	a_box,
		GodunovPhysics *	a_physPtr
	)

Compute high-order face-centered velocity divergence for artificial viscosity.

Computes a face-centered nonlinear function of the divergence suitable for use as an artificial viscosity coefficient for a fourth-order method.

F_visc = -dx*K*dU/dx K = max(-dx*div(u)*min(1,h^2*|div(u)/(c^2)/a_M0sq|),0)

void GodunovUtilities::deconvolve	(	FArrayBox &	a_avgFab,
		const FArrayBox &	a_cellFab,
		int	a_sign = `1`
	)

Deconvolve from cell-centered to cell-averaged data (or vice versa).

Deconvolves (or convolves, if a_sign = -1) by the formula

a_avgFab += a_sign * laplacian(a_cellFab) * m_dx^2 / 24, on a_cellFab.box()

void GodunovUtilities::deconvolve	(	FArrayBox &	a_avgFab,
		const FArrayBox &	a_cellFab,
		const Box &	a_box,
		int	a_sign = `1`
	)

Deconvolve from cell-centered to cell-averaged data (or vice versa) on a specified box.

Deconvolves (or convolves, if a_sign = -1) by the formula

a_avgFab += a_sign * laplacian(a_cellFab) * m_dx^2 / 24, on a_box

void GodunovUtilities::deconvolveFace	(	FluxBox &	a_avgFlux,
		const FluxBox &	a_cellFlux,
		int	a_sign = `1`
	)

Deconvolve from face-centered to face-averaged data (or vice versa).

Deconvolves (or convolves, if a_sign = -1) by the formula

a_avgFlux += a_sign * laplacian(a_cellFlux) * m_dx^2 / 24, on faces of a_cellFlux.box()

void GodunovUtilities::deconvolveFace	(	FluxBox &	a_avgFlux,
		const FluxBox &	a_cellFlux,
		const Box &	a_box,
		int	a_sign = `1`
	)

Deconvolve from face-centered to face-averaged data (or vice versa) on a specified box.

Deconvolves (or convolves, if a_sign = -1) by the formula

a_avgFlux += a_sign * laplacian(a_cellFlux) * m_dx^2 / 24, on faces of a_box

void GodunovUtilities::operator= ( const GodunovUtilities & ) [private]

Member Data Documentation

ProblemDomain GodunovUtilities::m_domain [protected]

Real GodunovUtilities::m_dx [protected]

bool GodunovUtilities::m_isDefined [protected]

bool GodunovUtilities::m_highOrderLimiter [protected]

Referenced by useHighOrderLimiter().

The documentation for this class was generated from the following file:

GodunovUtilities.H

GodunovUtilities Class Reference

Detailed Description

Public Member Functions

Protected Attributes

Private Member Functions

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation