Mapping from spherical coordinates (Xi) to real coodinates. More...

#include <RThetaPhiCS.H>

Inheritance diagram for RThetaPhiCS:

Public Member Functions
	RThetaPhiCS (const RealVect &a_dx, const Real a_stretch=1., const Real a_rMin=1., const Real a_phiMin=Pi/4.)
	Constructor. More...

virtual	~RThetaPhiCS ()
	Destructor. More...

virtual RealVect	realCoord (const RealVect &a_hatXi) const
	Given coordinate in mapped space, return its location in real space. More...

virtual RealVect	mappedCoord (const RealVect &a_x) const
	Given coordinate in real space, return its location in the mapped space. More...

virtual Real	dXdXi (const RealVect &a_Xi, int a_dirX, int a_dirXi) const
	note that a_Xi is in mapped space. More...

Public Member Functions inherited from NewFourthOrderCoordSys
	NewFourthOrderCoordSys ()
	default constructor More...

virtual	~NewFourthOrderCoordSys ()

virtual void	realCoord (FArrayBox &a_x, const FArrayBox &a_Xi, const Box &a_box) const
	given coordinates in mapped space, return locations in real space More...

virtual void	mappedCoord (FArrayBox &a_Xi, const FArrayBox &a_x, const Box &a_box) const
	given coordinate in real space, return its location in the mapped space More...

virtual void	getNodeRealCoordinates (FArrayBox &a_nodeCoords, const Box &a_box) const
	return Cartesian XYZ locations of nodes More...

virtual void	dXdXi (FArrayBox &a_dxdXi, const FArrayBox &a_Xi, int a_destComp, int a_dirX, int a_dirXi, const Box &a_box) const
	note that a_X is in mapped space. More...

virtual int	getNumN () const
	returns number of components in the metric term matrix (N) More...

virtual int	getNcomponent (const int a_row, const int a_col) const
	index function into face-centered metric terms More...

virtual void	volFlux (FluxBox &a_volFlux, const FluxBox &a_Nt, const Box &a_box) const
	computes the volume flux on the faces More...

virtual void	cellVol (FArrayBox &a_vol, const FluxBox &a_N, const Box &a_box) const
	computes cell volumes More...

virtual void	getN (FluxBox &a_N, const Box &a_box) const
	computes integral of N over each face of a_box More...

virtual void	getAvgJ (FArrayBox &a_avgJ, const FluxBox &a_volFlux, const Box &a_box) const
	computes cell-averaged J More...

virtual void	getAvgJ (FArrayBox &a_avgJ, const Box &a_box) const
	computes cell-averaged J More...

virtual void	getAvgJinverse (FluxBox &a_avgJinverse, const Box &a_box) const
	computes cell-averaged 1/J More...

virtual void	getAvgJinverse (FluxBox &a_avgJinverse, const FArrayBox &a_avgJ, const Box &a_box) const
	computes cell-averaged 1/J, using pre-computed cell-avg J More...

virtual Real	pointwiseJ (const RealVect &a_Xi) const
	Jacobian evaluated at location Xi in mapped space. More...

virtual void	pointwiseJ (FArrayBox &a_J, const FArrayBox &a_Xi, const Box &a_box) const
	Jacobian evaluated at locations Xi in mapped space. More...

virtual void	computeMetricTermProductAverage (FluxBox &a_product, const FluxBox &a_F, const FluxBox &a_N, const int a_NNumComp, const FluxBox &a_FforGrad, const Box &a_box, bool a_fourthOrder=true, Interval a_varIntervalProduct=Interval(), Interval a_varIntervalF=Interval(), int a_fluxSpaceContiguous=1, const ProblemDomain *const a_problemDomainPtr=NULL) const
	Computes 4th-order average of product = N^T*F. F can be a flux dyad. More...

virtual void	computeMetricTermProductAverage (FluxBox &a_product, const FluxBox &a_F, const FluxBox &a_N, const FluxBox &a_FforGrad, const Box &a_box, bool a_fourthOrder=true) const
	computes 4th-order average of product = N^T*F. F is vector of a scalar More...

virtual void	computeMetricTermProductAverage (FluxBox &a_product, const FluxBox &a_F, const FluxBox &a_N, const Box &a_box, bool a_fourthOrder=true) const
	computes 4th-order average of product = N^T*F. F is vector of a scalar More...

void	magnitudeN (FluxBox &a_NMag, const FluxBox &a_N, const Box &a_box) const
	Computes magnitude of <N^T> on each face. More...

virtual void	computeNJinverse (FluxBox &a_NJinverse, const FluxBox &a_Jinverse, const FluxBox &a_N, const Box &a_cellBox) const
	given N and Jinverse, computes N/J More...

virtual const RealVect &	dx () const
	access function to simplify things – returns mapped-space cell spacing More...

virtual Real	getN (const RealVect &a_Xi, int a_s, int a_d, int a_d1) const
	this evaluates the script N values from equation 12 in Phil's notes More...

virtual Real	getNMatrixEntry (const RealVect &a_Xi, int a_s, int a_d, int a_d1, int a_row, int a_column) const
	note that a_Xi is in mapped space. More...

virtual void	integrateScriptN (FArrayBox &a_scrN, const int a_dir0, const int a_dir1, const Box &a_box) const

virtual void	incrementFaceMetricWithEdgeTerm (FArrayBox &a_faceMetrics, int a_faceDir, int a_edgeDir, const Box &a_box, const Side::LoHiSide &a_side) const

virtual void	computeTransverseFaceMetric (FArrayBox &a_faceMetrics, const Box &a_box, int a_faceDir, int a_dDir) const

virtual void	computeTangentialGrad (FluxBox &a_gradPhi, const FluxBox &a_phiFace, const Box &a_box) const

virtual int	tanGradComp (const int a_faceDir, const int a_tanDir, const int a_comp) const

virtual void	contravariantMetric (FArrayBox &a_metric, int a_dir) const
	return row a_idir of contravariant metric More...

virtual void	orthonormalize (FluxBox &a_flux, const Interval &a_vectorIntv) const
	convert vector components (in a_vectorIntv) of a_flux to orthonormal frame to that of this block More...

virtual void	orthonormalize (FArrayBox &a_fluxFab, const Interval &a_vectorIntv) const
	overwrite vector components (in a_vectorIntv) of a_fluxFab with orthonormalized More...

virtual void	orthonormalize (const FArrayBox &a_csFab, FArrayBox &a_orthoFab, const Box &a_box, int a_idir, const IntVect &a_csComps, const IntVect &a_orthoComps) const
	convert components in a_csComps of vector a_csFab in coordinate-system basis to components in a_orthoComps of vector a_orthoFab in orthonormal basis, at points with indices in a_box, on lines where direction a_idir is constant More...

virtual void	deorthonormalize (FluxBox &a_flux, const Interval &a_vectorIntv) const
	convert vector components (in a_vectorIntv) of a_flux from orthonormal frame to that of this block More...

virtual void	deorthonormalize (FArrayBox &a_fluxFab, const Interval &a_vectorIntv) const
	overwrite vector components (in a_vectorIntv) of a_fluxFab with deorthonormalized More...

virtual void	deorthonormalize (const FArrayBox &a_orthoFab, FArrayBox &a_csFab, const Box &a_box, int a_idir, const IntVect &a_orthoComps, const IntVect &a_csComps) const
	convert components in a_orthoComps of vector a_orthoFab in orthonormal basis to components in a_csComps of vector a_csFab in coordinate-system basis, at points with indices in a_box, on lines where direction a_idir is constant More...

Public Member Functions inherited from NewCoordSys
	NewCoordSys ()
	default constructor More...

virtual	~NewCoordSys ()

virtual void	getCenterMappedCoordinates (FArrayBox &a_Xi, const Box &a_box) const
	given indices in a_box, return centers of cells (or of faces, or of edges) in mapped coordinates. The function does the right thing based on the centering of a_box, which must be the same centering as a_Xi. More...

virtual RealVect	centerMappedCoordinates (const IntVect &a_iv) const
	given indices, return centers of cells in mapped coordinates More...

virtual int	dimension () const
	returns dimensionality of the space More...

virtual void	computeDivergence (FArrayBox &a_divF, const FluxBox &a_F, const FluxBox &a_N, const Box &a_box, Interval &divInterval) const
	returns integral of divergence over mapped-grid cells More...

virtual VectorTransformation	vectorTransformationMappedToReal (const RealVect &a_Xi) const
	return matrix that transforms vector components from mapped space to real space at point a_Xi in mapped space More...

virtual VectorTransformation	vectorTransformationRealToMapped (const RealVect &a_Xi) const
	return matrix that transforms vector components from real space to mapped space at point a_Xi in mapped space More...

virtual VectorTransformation	vectorTransformationMappedToRealCenter (const IntVect &a_iv) const
	return matrix that transforms vector components from mapped space to real space at center of cell a_iv More...

virtual VectorTransformation	vectorTransformationRealToMappedCenter (const IntVect &a_iv) const
	return matrix that transforms vector components from real space to mapped space at center of cell a_iv More...

virtual void	vectorTransformMappedToRealCenterFab (FArrayBox &a_vectorFab) const
	transform a FAB of SpaceDim-vectors from mapped-coordinate basis to real-coordinate basis at cell centers More...

virtual void	vectorTransformMappedToRealAvgFab (FArrayBox &a_vectorFab, const FArrayBox &a_gradVectorFab) const
	transform a FAB of SpaceDim-vectors from mapped-coordinate basis to real-coordinate basis, averaged over cells More...

virtual void	vectorTransformRealToMappedCenterFab (FArrayBox &a_vectorFab) const
	transform a FAB of SpaceDim-vectors from real-coordinate basis to mapped-coordinate basis at cell centers More...

virtual void	vectorTransformRealToMappedAvgFab (FArrayBox &a_vectorFab, const FArrayBox &a_gradVectorFab) const
	transform a FAB of SpaceDim-vectors from real-coordinate basis to mapped-coordinate basis, averaged over cells More...

virtual void	setTime (const Real &a_time) const
	Set time for moving grids. More...

Protected Attributes
Real	m_stretch
	Stretching in the r direction. More...

Real	m_rMin
	Min r (> 0 avoids singularity there) More...

Real	m_phiMin

Protected Attributes inherited from NewFourthOrderCoordSys
RealVect	m_dx

Interval	m_volInterval

EdgeQuadrature *	m_quadraturePtr

Protected Attributes inherited from NewCoordSys
Real	m_time
	Const is already well entrenched. More...

Private Member Functions
RealVect	normalize (const RealVect &a_Xi) const
	Normalize the mapped coordinates $(0 <= \hat{\xi} <= 1)$ . More...

RealVect	unnormalize (const RealVect &a_hatXi) const
	Unnormalized the mapped coordinates. More...

RealVect	realCoordUN (const RealVect &a_Xi) const
	Return location in real space of an unnormalized Coord. from mapped space. More...

Additional Inherited Members
Static Public Member Functions inherited from NewFourthOrderCoordSys
static const IntVect &	metricsCompDir (const int a_iDir)
	Same as getNcomponent but returns an IntVect for an 'a_col' (direction) More...

Protected Member Functions inherited from NewCoordSys
virtual void	vectorTransformInternalAvgFab (FArrayBox &a_vectorFab, const FArrayBox &a_gradVectorFab, const BaseFab< VectorTransformation > &a_tfmCenterFab) const
	internal function to transform a FAB of SpaceDim-vectors from one basis to another, averaged over cells, given BaseFab of vector transformations at cell centers More...

Detailed Description

Mapping from spherical coordinates (Xi) to real coodinates.

$\theta$ is the azimuthal angle (counter-clockwise from +x axis in xy plane)
$\varphi$ is the inclination angle measure from +z axis

$x = r\sin\varphi\cos\theta$
$y = r\sin\varphi\sin\theta$
$z = r\cos\varphi$

But to avoid singularities, we define
$r = \mbox(stretch)(\hat(r) + r_(\min))$
$\theta = 2\pi\hat(\theta)$
$\varphi = \hat(\varphi)(\pi - 2\varphi_(\min)) + \varphi_(\min)$
where $0 <= \hat(r), \hat(\theta), \hat(\varphi) <= 1$ . stretch, $r_(\min)$ , and $\varphi_(\min)$ are defined by input. Note that $\varphi_(\min)$ is the minimum angle with the z-axis.

Constructor & Destructor Documentation

◆ RThetaPhiCS()

RThetaPhiCS::RThetaPhiCS	(	const RealVect &	a_dx,
		const Real	a_stretch = `1.`,
		const Real	a_rMin = `1.`,
		const Real	a_phiMin = `Pi/4.`
	)

Constructor.

◆ ~RThetaPhiCS()

virtual RThetaPhiCS::~RThetaPhiCS ( )

virtual

Destructor.

Member Function Documentation

◆ realCoord()

virtual RealVect RThetaPhiCS::realCoord ( const RealVect & a_hatXi ) const

virtual

Given coordinate in mapped space, return its location in real space.

Implements NewFourthOrderCoordSys.

◆ mappedCoord()

virtual RealVect RThetaPhiCS::mappedCoord ( const RealVect & a_x ) const

virtual

Given coordinate in real space, return its location in the mapped space.

Implements NewFourthOrderCoordSys.

◆ dXdXi()

virtual Real RThetaPhiCS::dXdXi	(	const RealVect &	a_Xi,
		int	a_dirX,
		int	a_dirXi
	)		const

virtual

note that a_Xi is in mapped space.

Implements NewFourthOrderCoordSys.

◆ normalize()

RealVect RThetaPhiCS::normalize ( const RealVect & a_Xi ) const

private

Normalize the mapped coordinates $(0 <= \hat{\xi} <= 1)$ .

◆ unnormalize()

RealVect RThetaPhiCS::unnormalize ( const RealVect & a_hatXi ) const

private

Unnormalized the mapped coordinates.

◆ realCoordUN()

RealVect RThetaPhiCS::realCoordUN ( const RealVect & a_Xi ) const

private

Return location in real space of an unnormalized Coord. from mapped space.

Member Data Documentation

◆ m_stretch

Real RThetaPhiCS::m_stretch

protected

Stretching in the r direction.

◆ m_rMin

Real RThetaPhiCS::m_rMin

protected

Min r (> 0 avoids singularity there)

◆ m_phiMin

Real RThetaPhiCS::m_phiMin

protected

Min angle between r and z-axis. (>0 avoids singularity there)

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

RThetaPhiCS.H

Public Member Functions

Protected Attributes

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RThetaPhiCS()

◆ ~RThetaPhiCS()

Member Function Documentation

◆ realCoord()

◆ mappedCoord()

◆ dXdXi()

◆ normalize()

◆ unnormalize()

◆ realCoordUN()

Member Data Documentation

◆ m_stretch

◆ m_rMin

◆ m_phiMin