RThetaPhiCS Class Reference

#include <RThetaPhiCS.H>

Inheritance diagram for RThetaPhiCS:

Inheritance graph
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List of all members.


Detailed Description

Mapping from spherical coordinates (Xi) to real coodinates.

$ 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.

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.
virtual ~RThetaPhiCS ()
 Destructor.
virtual RealVect realCoord (const RealVect &a_hatXi) const
 Given coordinate in mapped space, return its location in real space.
virtual RealVect mappedCoord (const RealVect &a_x) const
 Given coordinate in real space, return its location in the mapped space.
virtual Real dXdXi (const RealVect &a_Xi, int a_dirX, int a_dirXi) const
 note that a_Xi is in mapped space.

Protected Attributes

Real m_stretch
 Stretching in the r direction.
Real m_rMin
 Min r (> 0 avoids singularity there).
Real m_phiMin

Private Member Functions

RealVect normalize (const RealVect &a_Xi) const
 Normalize the mapped coordinates $(0 <= \hat{\xi} <= 1)$.
RealVect unnormalize (const RealVect &a_hatXi) const
 Unnormalized the mapped coordinates.
RealVect realCoordUN (const RealVect &a_Xi) const
 Return location in real space of an unnormalized Coord. from mapped space.


Constructor & Destructor Documentation

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

Constructor.

virtual RThetaPhiCS::~RThetaPhiCS (  )  [virtual]

Destructor.


Member Function Documentation

virtual RealVect RThetaPhiCS::realCoord ( const RealVect a_hatXi  )  const [virtual]

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

Implements NewFourthOrderCoordSys.

virtual RealVect RThetaPhiCS::mappedCoord ( const RealVect a_x  )  const [virtual]

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

Implements NewFourthOrderCoordSys.

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.

RealVect RThetaPhiCS::normalize ( const RealVect a_Xi  )  const [private]

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

RealVect RThetaPhiCS::unnormalize ( const RealVect a_hatXi  )  const [private]

Unnormalized the mapped coordinates.

RealVect RThetaPhiCS::realCoordUN ( const RealVect a_Xi  )  const [private]

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


Member Data Documentation

Stretching in the r direction.

Min r (> 0 avoids singularity there).

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


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

Generated on Wed Mar 29 03:27:17 2017 for Chombo + EB + MF by  doxygen 1.5.5