Density diffusion flux for the MHD model. More...

#include <density_diffusion_flux.h>

Inheritance diagram for wxm::apps::rmhd::DensityDiffusionFlux:

Detailed Description

Density diffusion flux for the MHD model.

In Euler or MHD fluid systems, the diffusion of density is driven indirectly through pressure gradients and inter- or intra- species collisional processes (viscosity, resisitivity, etc.).

In some cases, enhanced density diffusion may be desirable for stability purposes or to approximate processes not captured by the model.

Density diffusion flux

The density diffusion flux in conservative form

\[ \frac{\partial \rho_p}{\partial t} = - \nabla \cdot (-D \nabla \rho_p ) \]

where \(D\) is the diffusion coefficient (see options for the calculation of \(D\) below), and the flux vector in cartesian cooridnates

\[ \overline{\overline{\mathcal{F}}} = \begin{bmatrix} - D \frac{\partial \rho_p}{\partial x} & - D \frac{\partial \rho_p}{\partial y} & - D \frac{\partial \rho_p}{\partial z} \\ 0 & 0 & 0 \\ \vdots & \vdots & \vdots \end{bmatrix} \]

Diffusion coefficient options

The diffusion coefficient can have the following forms:

_ddiff_type == "basic". Constant density diffusion coefficient
\[ D_{basic} = \text{_ddiff}. \]
_ddiff_type == "nimrod". A NIMROD-style density diffusion, where diffusion is a funciton of the density gradient
\[ D_{nim} = \min(\text{_ddiff} \cdot dx^2 \; |v \cdot \nabla n / n|, \; \text{_ddiff_limit}) \]

The suggested maximum time step is given by

\[ \Delta t_{\max} = CFL_{diff} \frac{\Delta x_{eff}^2}{D} \]

where

\[ \Delta x_{eff} = CFL \Delta x. \]

Cylindrical coordinates

In the case of density diffusion in cylindrical coordinates, cylindrical source terms are necessary. This app must be used in conjuction with density_diffusion_cyl_source.

See also: Warpy constructor: warpy.apps.mhd.rmhd.rmhd.density_diffusion_flux_mhd

Public Types
enum	GradientMethod { LDG }
	Available gradient methods. More...

enum	DDiffType { BASIC , NIMROD }
	Available density diffusion types. More...

Public Types inherited from WmApplication
typedef Application_Variable	WmApplication_Variable

typedef std::map< std::string, std::string >	replaceMap_t

Public Member Functions
	DensityDiffusionFlux ()

	~DensityDiffusionFlux () override

void	setup (const WxCryptSet &wxc) override
	Setup.

const std::vector< int > &	getInputVariableIndexes (int flag) const override
	Grab input variable indices.

const std::vector< int > &	getAuxiliaryVariableIndexes (int flag) const override
	Grab auxiliary variable indices.

const std::vector< int > &	getOutputVariableIndexes (int flag) const override
	Grab output variable indices.

real	numerical_flux (const real q_l, const real q_r, const real aux_l, const real aux_r, const solverVariables_t pFV, real numericalFlux) const override
	Redefinition of the numerical flux function.

real	internal_flux (const real q, const real aux, const solverVariables_t *pSV, std::vector< std::vector< real > > &internalFlux) const override
	Redefinition of the interal flux function.

real	numerical_flux_ldg (const real q_l, const real q_r, const real aux_l, const real aux_r, const solverVariables_t pFV, real numericalFlux) const
	The numerical flux function using the LDG gradient method.

Public Member Functions inherited from WmApplication
	WmApplication ()

virtual	~WmApplication ()=default

virtual void	setup (const WxCryptSet &wxc)

virtual const std::vector< int > &	getAuxiliaryVariableIndexes (int flag=WMAPPLICATIONFLAG_NONE) const

virtual const std::vector< int > &	getCrossVariableIndexes (int flag=WMAPPLICATIONFLAG_NONE) const

const std::vector< std::string > &	getBoundaryNames () const

bool	isOnBoundary (const std::string &boundaryName) const

bool	has (int flag) const

virtual real	numerical_flux (const real q_l, const real q_r, const real aux_l, const real aux_r, const solverVariables_t pFV, real numericalFlux) const

virtual real	internal_flux (const real q, const real aux, const solverVariables_t *pSV, std::vector< std::vector< real > > &internalFlux) const

virtual real	source (const real q, const real aux, const elementGeometry_t pEG, real source) const

virtual void	bc_q (const real q_in, const real aux_in, const real aux_out, const solverVariables_t pFV, real *q_out) const
	Boundary Condition Application which sets the boundary condition on ghost nodes.

virtual real	bcNumericalFlux (const real q_l, const real q_r, const real aux_l, const real aux_r, const solverVariables_t pFV, real numericalFlux) const

virtual void	conserved_to_primitive (const real q, const real aux, real *w) const

virtual void	primitive_to_conserved (const real w, const real aux, real *q) const

virtual void	evaluate_function (const real q, const real aux, const solverVariables_t pSV, real result) const

virtual void	bc_q_kinetic (const real q_in, const real aux_in, const solverVariables_t pFV, real q_out) const

std::shared_ptr< std::string >	app_name ()

virtual const std::vector< int > &	getInputVariableIndexes (int flag=0) const

virtual const std::vector< int > &	getOutputVariableIndexes (int flag=0) const

Protected Attributes
GradientMethod	_gradient_method
	Gradient method chosen for app.

DDiffType	_ddiff_type
	Density diffusion type.

std::vector< int >	_input_variables
	Vector of MHD fluid variable indices.

std::vector< int >	_aux_variables
	Vector of MHD fluid gradient variable indices.

real	_ddiff
	Density diffusion coefficient.

real	_ddiff_limit
	Density diffusion coefficient limit for Nimrod method.

real	_cfl_diff
	Diffusion CFL.

std::vector< std::vector< real > >	_flux_tensor
	Flux tensor is used to calculate left and right fluxes for numerical flux mutable because this will continuously be changed upon call, but functions are labled const.

Protected Attributes inherited from WmApplication
std::string	_app_name

WxLogStream	_debStrm

std::vector< int >	_allowedFlags

std::vector< std::string >	_onBoundaries

Additional Inherited Members
Static Public Attributes inherited from wxm::app_base
static std::vector< int >	empty

Protected Member Functions inherited from wxm::app_base
virtual	~app_base ()=default

Member Enumeration Documentation

◆ DDiffType

enum wxm::apps::rmhd::DensityDiffusionFlux::DDiffType

Available density diffusion types.

Enumerator
BASIC
NIMROD

◆ GradientMethod

enum wxm::apps::rmhd::DensityDiffusionFlux::GradientMethod

Available gradient methods.

Enumerator
LDG

Constructor & Destructor Documentation

◆ DensityDiffusionFlux()

wxm::apps::rmhd::DensityDiffusionFlux::DensityDiffusionFlux ( )

◆ ~DensityDiffusionFlux()

wxm::apps::rmhd::DensityDiffusionFlux::~DensityDiffusionFlux ( )

override

Member Function Documentation

◆ getAuxiliaryVariableIndexes()

const std::vector< int > & wxm::apps::rmhd::DensityDiffusionFlux::getAuxiliaryVariableIndexes ( int flag ) const

inlineoverridevirtual

Grab auxiliary variable indices.

Parameters

int	flag - usually flag is given like flux type but usually not checked

Returns: vector of output variable indices

Reimplemented from WmApplication.

◆ getInputVariableIndexes()

const std::vector< int > & wxm::apps::rmhd::DensityDiffusionFlux::getInputVariableIndexes ( int flag ) const

inlineoverridevirtual

Grab input variable indices.

Parameters

int	flag - usually flag is given like flux type but usually not checked

Returns: vector of input variable indices

Reimplemented from wxm::app_base.

◆ getOutputVariableIndexes()

const std::vector< int > & wxm::apps::rmhd::DensityDiffusionFlux::getOutputVariableIndexes ( int flag ) const

inlineoverridevirtual

Grab output variable indices.

Parameters

int	flag - usually flag is given like flux type but usually not checked

Returns: vector of output variable indices

Reimplemented from wxm::app_base.

◆ internal_flux()

real wxm::apps::rmhd::DensityDiffusionFlux::internal_flux	(	const real *	q,
		const real *	aux,
		const solverVariables_t *	pSV,
		std::vector< std::vector< real > > &	internalFlux
	)		const

overridevirtual

Redefinition of the interal flux function.

Parameters

const	q - input variable
const	aux - auxiliary variable
const	pSV - solver variable structure
const	internalFlux - 2D vector of internal fluxes
result	- suggested dt

Reimplemented from WmApplication.

◆ numerical_flux()

real wxm::apps::rmhd::DensityDiffusionFlux::numerical_flux	(	const real *	q_l,
		const real *	q_r,
		const real *	aux_l,
		const real *	aux_r,
		const solverVariables_t *	pFV,
		real *	numericalFlux
	)		const

overridevirtual

Redefinition of the numerical flux function.

Parameters

const	q_l - input variable, left
const	q_r - input variable, right
const	aux_l - auxiliary variable, left
const	aux_r - auxiliary variable, right
const	pFV - solver variable structure
const	numericalFlux - numerical fluxes
result	- suggested dt

Reimplemented from WmApplication.

◆ numerical_flux_ldg()

real wxm::apps::rmhd::DensityDiffusionFlux::numerical_flux_ldg	(	const real *	q_l,
		const real *	q_r,
		const real *	aux_l,
		const real *	aux_r,
		const solverVariables_t *	pFV,
		real *	numericalFlux
	)		const

The numerical flux function using the LDG gradient method.

Parameters

const	q_l - input variable, left
const	q_r - input variable, right
const	aux_l - auxiliary variable, left
const	aux_r - auxiliary variable, right
const	pFV - solver variable structure
const	numericalFlux - 2D vector of numerical fluxes
result	- suggested dt

◆ setup()

void wxm::apps::rmhd::DensityDiffusionFlux::setup ( const WxCryptSet & wxc )

overridevirtual

Setup.

Parameters

WxCryptSet object

Reimplemented from WmApplication.

Member Data Documentation

◆ _aux_variables

std::vector<int> wxm::apps::rmhd::DensityDiffusionFlux::_aux_variables

protected

Vector of MHD fluid gradient variable indices.

Len 24.

◆ _cfl_diff

real wxm::apps::rmhd::DensityDiffusionFlux::_cfl_diff

protected

Diffusion CFL.

◆ _ddiff

real wxm::apps::rmhd::DensityDiffusionFlux::_ddiff

protected

Density diffusion coefficient.

◆ _ddiff_limit

real wxm::apps::rmhd::DensityDiffusionFlux::_ddiff_limit

protected

Density diffusion coefficient limit for Nimrod method.

◆ _ddiff_type

DDiffType wxm::apps::rmhd::DensityDiffusionFlux::_ddiff_type

protected

Density diffusion type.

See class description.

◆ _flux_tensor

std::vector<std::vector<real> > wxm::apps::rmhd::DensityDiffusionFlux::_flux_tensor

mutableprotected

Flux tensor is used to calculate left and right fluxes for numerical flux mutable because this will continuously be changed upon call, but functions are labled const.

◆ _gradient_method

GradientMethod wxm::apps::rmhd::DensityDiffusionFlux::_gradient_method

protected

Gradient method chosen for app.

◆ _input_variables

std::vector<int> wxm::apps::rmhd::DensityDiffusionFlux::_input_variables

protected

Vector of MHD fluid variable indices.

Len 8.

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

src/apps/mhd/rmhd/density_diffusion_flux.h

Detailed Description

Density diffusion flux

Diffusion coefficient options

The suggested maximum time step is given by

Cylindrical coordinates

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ DDiffType

◆ GradientMethod

Constructor & Destructor Documentation

◆ DensityDiffusionFlux()

◆ ~DensityDiffusionFlux()

Member Function Documentation

◆ getAuxiliaryVariableIndexes()

◆ getInputVariableIndexes()

◆ getOutputVariableIndexes()

◆ internal_flux()

◆ numerical_flux()

◆ numerical_flux_ldg()

◆ setup()

Member Data Documentation

◆ _aux_variables

◆ _cfl_diff

◆ _ddiff

◆ _ddiff_limit

◆ _ddiff_type

◆ _flux_tensor

◆ _gradient_method

◆ _input_variables