File paralleltransform.hxx

class ParallelTransform
#include <paralleltransform.hxx>

Calculates the values of a field along the magnetic field (y direction)

This is used inside Mesh to represent a variety of possible numerical schemes, including Shifted Metric and FCI

Subclassed by FCITransform, ParallelTransformIdentity, ShiftedMetric, ShiftedMetricInterp

Public Functions

inline ParallelTransform(Mesh &mesh_in, Options *opt = nullptr)
virtual ~ParallelTransform() = default
virtual void calcParallelSlices(Field3D &f) = 0

Given a 3D field, calculate and set the Y up down fields.

inline virtual void integrateParallelSlices(Field3D &f)

Calculate Yup and Ydown fields by integrating over mapped points This should be used for parallel divergence operators

virtual Field3D toFieldAligned(const Field3D &f, const std::string &region = "RGN_ALL") = 0

Convert a field into field-aligned coordinates so that the y index is along the magnetic field

virtual FieldPerp toFieldAligned(const FieldPerp &f, const std::string &region = "RGN_ALL") = 0
virtual Field3D fromFieldAligned(const Field3D &f, const std::string &region = "RGN_ALL") = 0

Convert back from field-aligned coordinates into standard form

virtual FieldPerp fromFieldAligned(const FieldPerp &f, const std::string &region = "RGN_ALL") = 0
inline virtual Field2D toFieldAligned(const Field2D &f, const std::string &region = "RGN_ALL")

Field2D are axisymmetric, so transformation to or from field-aligned coordinates is a null operation.

inline virtual Field2D fromFieldAligned(const Field2D &f, const std::string &region = "RGN_ALL")
virtual bool canToFromFieldAligned() = 0
inline virtual std::vector<PositionsAndWeights> getWeightsForYUpApproximation(int i, int j, int k)
inline virtual std::vector<PositionsAndWeights> getWeightsForYDownApproximation(int i, int j, int k)
inline virtual std::vector<PositionsAndWeights> getWeightsForYApproximation(int i, int j, int k, int yoffset)
inline virtual void outputVars(Datafile &file)

Output variables used by a ParallelTransform instance to the dump files.

virtual bool requiresTwistShift(bool twist_shift_enabled, YDirectionType ytype) = 0

If twist_shift_enabled is true, does a Field3D with Y direction ytype require a twist-shift at branch cuts on closed field lines?

Protected Functions

virtual void checkInputGrid() = 0

This method should be called in the constructor to check that if the grid has a ‘parallel_transform’ variable, it has the correct value

Protected Attributes

Mesh &mesh

The mesh this paralleltransform is part of.

Options &options

Options for this ParallelTransform.

struct PositionsAndWeights

Public Members

int i
int j
int k
BoutReal weight
class ParallelTransformIdentity : public ParallelTransform
#include <paralleltransform.hxx>

This class implements the simplest form of ParallelTransform where the domain is a logically rectangular domain, and yup() and ydown() refer to the same field.

Public Functions

inline ParallelTransformIdentity(Mesh &mesh_in, Options *opt = nullptr)
virtual void calcParallelSlices(Field3D &f) override

Merges the yup and ydown() fields of f, so that f.yup() = f.ydown() = f

inline virtual Field3D toFieldAligned(const Field3D &f, const std::string &region = "RGN_ALL") override

The field is already aligned in Y, so this does nothing

inline virtual FieldPerp toFieldAligned(const FieldPerp &f, const std::string &region = "RGN_ALL") override
inline virtual Field3D fromFieldAligned(const Field3D &f, const std::string &region = "RGN_ALL") override

The field is already aligned in Y, so this does nothing

inline virtual FieldPerp fromFieldAligned(const FieldPerp &f, const std::string &region = "RGN_ALL") override
inline virtual std::vector<PositionsAndWeights> getWeightsForYApproximation(int i, int j, int k, int yoffset) override
inline virtual bool canToFromFieldAligned() override
inline virtual bool requiresTwistShift(bool twist_shift_enabled, YDirectionType ytype) override

If twist_shift_enabled is true, does a Field3D with Y direction ytype require a twist-shift at branch cuts on closed field lines?

Protected Functions

virtual void checkInputGrid() override

This method should be called in the constructor to check that if the grid has a ‘parallel_transform’ variable, it has the correct value

class ShiftedMetric : public ParallelTransform
#include <paralleltransform.hxx>

Shifted metric method Each Y location is shifted in Z with respect to its neighbours so that the grid is orthogonal in X-Z, but requires interpolation to calculate the values of points along field-lines.

In this implementation the interpolation is done using FFTs in Z

Public Functions

ShiftedMetric() = delete
ShiftedMetric(Mesh &mesh, CELL_LOC location, Field2D zShift, BoutReal zlength_in, Options *opt = nullptr)
virtual void calcParallelSlices(Field3D &f) override

Calculates the yup() and ydown() fields of f by taking FFTs in Z and applying a phase shift.

virtual Field3D toFieldAligned(const Field3D &f, const std::string &region = "RGN_ALL") override

Uses FFTs and a phase shift to align the grid points with the y coordinate (along magnetic field usually).

Note that the returned field will no longer be orthogonal in X-Z, and the metric tensor will need to be changed if X derivatives are used.

Shift the field so that X-Z is not orthogonal, and Y is then field aligned.

virtual FieldPerp toFieldAligned(const FieldPerp &f, const std::string &region = "RGN_ALL") override
virtual Field3D fromFieldAligned(const Field3D &f, const std::string &region = "RGN_ALL") override

Converts a field back to X-Z orthogonal coordinates from field aligned coordinates.

Shift back, so that X-Z is orthogonal, but Y is not field aligned.

virtual FieldPerp fromFieldAligned(const FieldPerp &f, const std::string &region = "RGN_ALL") override
inline virtual std::vector<PositionsAndWeights> getWeightsForYApproximation(int i, int j, int k, int yoffset) override
inline virtual bool canToFromFieldAligned() override
virtual void outputVars(Datafile &file) override

Save zShift to the output.

inline virtual bool requiresTwistShift(bool twist_shift_enabled, YDirectionType ytype) override

If twist_shift_enabled is true, does a Field3D with Y direction ytype require a twist-shift at branch cuts on closed field lines?

Protected Functions

virtual void checkInputGrid() override

This method should be called in the constructor to check that if the grid has a ‘parallel_transform’ variable, it has the correct value

Private Functions

inline Field2D shiftZ(const Field2D &f, const Field2D &zangle, const std::string region = "RGN_NOX") const

Shift a 2D field in Z. Since 2D fields are constant in Z, this has no effect

Field3D shiftZ(const Field3D &f, const Field2D &zangle, const std::string &region = "RGN_NOX") const

Shift a 3D field f in Z by the given zangle

Parameters
  • f[in] The field to shift

  • zangle[in] Toroidal angle (z)

Field3D shiftZ(const Field3D &f, const Tensor<dcomplex> &phs, const YDirectionType y_direction_out, const std::string &region = "RGN_NOX") const

Shift a 3D field or FieldPerp f by the given phase phs in Z

Calculates FFT in Z, multiplies by the complex phase and inverse FFTS.

Parameters
  • f[in] The field to shift

  • phs[in] The phase to shift by

  • y_direction_out[in] The value to set yDirectionType of the result to

FieldPerp shiftZ(const FieldPerp &f, const Tensor<dcomplex> &phs, const YDirectionType y_direction_out, const std::string &region = "RGN_NOX") const
void shiftZ(const BoutReal *in, int len, BoutReal zangle, BoutReal *out) const

Shift a given 1D array, assumed to be in Z, by the given zangle

Parameters
  • in[in] A 1D array of length len

  • len[in] Length of the in and out arrays

  • zangle[in] The angle (z coordinate) to shift by

  • out[out] A 1D array of length len, already allocated

void shiftZ(const BoutReal *in, const dcomplex *phs, BoutReal *out) const

Shift a given 1D array, assumed to be in Z, by the given zangle

Parameters
  • in[in] A 1D array of length mesh.LocalNz

  • phs[in] Phase shift, assumed to have length (mesh.LocalNz/2 + 1) i.e. the number of modes

  • out[out] A 1D array of length mesh.LocalNz, already allocated

void cachePhases()

Calculate and store the phases for to/from field aligned and for the parallel slices using zShift

std::vector<Field3D> shiftZ(const Field3D &f, const std::vector<ParallelSlicePhase> &phases) const

Shift a 3D field f in Z to all the parallel slices in phases

Parameters
  • f[in] The field to shift

  • phases[in] The phase and offset information for each parallel slice

Returns

The shifted parallel slices

Private Members

CELL_LOC location = {CELL_CENTRE}
Field2D zShift

This is the shift in toroidal angle (z) which takes a point from X-Z orthogonal to field-aligned along Y.

BoutReal zlength = {0.}

Length of the z-domain in radians.

int nmodes
Tensor<dcomplex> toAlignedPhs

Cache of phase shifts for transforming from X-Z orthogonal coordinates to field-aligned coordinates

Tensor<dcomplex> fromAlignedPhs

Cache of phase shifts for transforming from field-aligned coordinates to X-Z orthogonal

std::vector<ParallelSlicePhase> parallel_slice_phases

Cache of phase shifts for the parallel slices. Slices are stored in the following order: {+1, …, +n, -1, …, -n} slice[i] stores offset i+1 slice[n + i] stores offset -(i+1) where i goes from 0 to (n-1), with n the number of y guard cells

struct ParallelSlicePhase

coordinates

Helper POD for parallel slice phase shifts

Public Members

Tensor<dcomplex> phase_shift
int y_offset