File fv_ops.hxx

namespace FV

Functions

const Field3D Div_a_Laplace_perp(const Field3D &a, const Field3D &x)

Div ( a Laplace_perp(x) ) Vorticity

const Field3D Div_par_K_Grad_par(const Field3D &k, const Field3D &f, bool bndry_flux = true)

Divergence of a parallel diffusion Div( k * Grad_par(f) )

const Field3D D4DY4(const Field3D &d, const Field3D &f)

4th-order derivative in Y, using derivatives on cell boundaries.

A one-sided 3rd-order derivative, given a value at a boundary is:

d3f/dx3 ~= 16/5 f_b - 6 f_0 + 4 f_1 - 6/5 f_2

where f_b is the value on the boundary; f_0 is the cell to the left of the boundary; f_1 to the left of f_0 and f_2 to the left of f_1

f_2 | f_1 | f_0 | f_b

NB: Uses to/from FieldAligned coordinates

const Field3D D4DY4_Index(const Field3D &f, bool bndry_flux = true)

4th-order dissipation term

A one-sided 3rd-order derivative, given a value at a boundary is:

d3f/dx3 ~= 16/5 f_b - 6 f_0 + 4 f_1 - 6/5 f_2

where f_b is the value on the boundary; f_0 is the cell to the left of the boundary; f_1 to the left of f_0 and f_2 to the left of f_1

f_2 | f_1 | f_0 | f_b

void communicateFluxes(Field3D &f)

Communicate fluxes between processors Takes values in guard cells, and adds them to cells

template<typename CellEdges = MC>
const Field3D Div_par(const Field3D &f_in, const Field3D &v_in, const Field3D &wave_speed_in, bool fixflux = true)

Finite volume parallel divergence

Preserves the sum of f*J*dx*dy*dz over the domain

NB: Uses to/from FieldAligned coordinates

Parameters
  • f_in: The field being advected. This will be reconstructed at cell faces using the given CellEdges method
  • v_in: The advection velocity. This will be interpolated to cell boundaries using linear interpolation
  • wave_speed_in: Local maximum speed of all waves in the system at each
  • fixflux: Fix the flux at the boundary to be the value at the midpoint (for boundary conditions)

template<typename CellEdges = MC>
const Field3D Div_f_v(const Field3D &n_in, const Vector3D &v, bool bndry_flux)

Div ( n * v ) Magnetic drifts

This uses the expression

Div( A ) = 1/J * d/di ( J * A^i )

Hence the input vector should be contravariant

Note: Uses to/from FieldAligned

struct Fromm
#include <fv_ops.hxx>

Fromm method

Public Functions

void operator()(Stencil1D &n)
struct MC
#include <fv_ops.hxx>

Monotonised Central (MC) second order slope limiter (Van Leer)

Limits the slope based on taking the slope with the minimum absolute value from central, 2*left and 2*right. If any of these slopes have different signs then the slope reverts to zero (i.e. 1st-order upwinding).

Public Functions

void operator()(Stencil1D &n)

Private Functions

BoutReal minmod(BoutReal a, BoutReal b, BoutReal c)
struct MinMod
#include <fv_ops.hxx>

Second order slope limiter method

Limits slope to minimum absolute value of left and right gradients. If at a maximum or minimum slope set to zero, i.e. reverts to first order upwinding

Public Functions

void operator()(Stencil1D &n)

Private Functions

BoutReal _minmod(BoutReal a, BoutReal b)

Internal helper function for minmod slope limiter

If the inputs have different signs then returns zero, otherwise chooses the value with the minimum magnitude.

struct Stencil1D
#include <fv_ops.hxx>

Stencil used for Finite Volume calculations which includes cell face values L and R

struct Upwind
#include <fv_ops.hxx>

First order upwind for testing

Public Functions

void operator()(Stencil1D &n)