File gyro_average.hxx#

Gyro-averaging operators

2010-09-03 Ben Dudson bd512@york.ac.uk

  • Initial version, simple averaging operator

Copyright 2010 B.D.Dudson, S.Farley, M.V.Umansky, X.Q.Xu

Contact: Ben Dudson, bd512@york.ac.uk

This file is part of BOUT++.

BOUT++ is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

BOUT++ is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with BOUT++. If not, see http://www.gnu.org/licenses/.

Functions

Field3D gyroTaylor0(const Field3D &f, const Field3D &rho)

Gyro-average using Taylor series approximation

\( \Gamma(f) = f + \rho^2 \nabla_\perp^2(f)\)

Note: Faster, but less robust than Pade approximations

Parameters:

  • f – [in] The field to gyro-average

  • rho – [in] Gyro-radius

Field3D gyroPade0(const Field3D &f, const Field3D &rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)

Gyro-average using Pade approximation

\( \Gamma_0 = (1 - \rho^2 \nabla_\perp^2)g = f\)

NOTE: Uses Z average of rho for efficient inversion

Parameters:

  • f – [in] The field to gyro-average

  • rho – [in] Gyro-radius

  • inner_boundary_flags – [in] Flags for the inner boundary to be passed to the Laplacian inversion operator

  • outer_boundary_flags – [in] Flags for the outer boundary to be passed to the Laplacian inversion operator

Field3D gyroPade0(const Field3D &f, const Field2D &rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)
Field3D gyroPade0(const Field3D &f, BoutReal rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)
Field3D gyroPade1(const Field3D &f, const Field3D &rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)

Pade approximation \(Gamma_1 = (1 - \frac{1}{2} \rho^2 \nabla_\perp^2)g = f\)

Note: Have to use Z average of rho for efficient inversion

Parameters:

  • f – [in] The field to gyro-average

  • rho – [in] Gyro-radius

  • inner_boundary_flags – [in] Flags for the inner boundary to be passed to the Laplacian inversion operator

  • outer_boundary_flags – [in] Flags for the outer boundary to be passed to the Laplacian inversion operator

Field3D gyroPade1(const Field3D &f, const Field2D &rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)
Field3D gyroPade1(const Field3D &f, BoutReal rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)
Field2D gyroPade1(const Field2D &f, const Field2D &rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)
Field3D gyroPade2(const Field3D &f, const Field3D &rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)

Pade approximation

\[ \Gamma_2(f) = \frac{1}{2}\rho^2 \nabla_\perp^2 ( 1 - \frac{1}{2} \rho^2 \nabla_\perp^2)^{-1}\Gamma_1(f) \]

Note: Have to use Z average of rho for efficient inversion

Parameters:

f – [in] The field to gyro-average

Param :

Field3D gyroPade2(const Field3D &f, const Field2D &rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)
Field3D gyroPade2(const Field3D &f, BoutReal rho, int inner_boundary_flags = GYRO_FLAGS, int outer_boundary_flags = GYRO_FLAGS)

Variables

constexpr int GYRO_FLAGS = INVERT_BNDRY_ONE + INVERT_RHS#

INVERT_BNDRY_ONE | INVERT_IN_RHS | INVERT_OUT_RHS; uses old-style Laplacian inversion flags