B-dependent diffusivity for MHD. More...

#include <bdependent_diffusivity_flux.h>

Inheritance diagram for wxm::apps::viscousmhd::BdependentDiffusivityFlux:

Detailed Description

B-dependent diffusivity for MHD.

This app is generally intended to be used instead of /src/apps/mhd/viscousmhd/wmapplication_intraspecies_collisions_mhd.h/cc although they could be "superimposed" if the user had some specific reason to do so.

The resulting diffusivities have B dependence similar to Braginskii viscous and thermal transport, with 1/B^2 dependence as seen in, e.g., Eqs. 2.12 and 2.13 of [Braginskii RPP Vol 1, 1965], which correspond to perpendicular thermal conductivities in the magnetized limit. See also discussion of a similar form for perpendicular transport in [Meier, UW dissertation (2011), Sec. 1.4].

For the associated cylindrical source term, see BdependentDiffusivityCylSource.

If the _B_ref variable is set to a value > 0, then diffusivity will be set as D = (D0 - D1) / ((B / B0)**2 + 1) + D1, where D represents either momentum or thermal diffusivity. This form leads to D --> D0 at small B, and --> D1 at large B. Generally, D1 < D0 is recommended.

If _B_ref is set to 0, D = D0.

The diffusivity value for momentum is converted to a dynamic viscosity (mu) when evaluating the stress tensor, and likewise thermal diffusivity is converted to a thermal conductivity (kappa) when evaluating thermal conduction.

Additional notes:

The value of D0 is set by either _const_Dmom or _const_Dtherm.
The value of D1 is set by the _D_min variable.
The _n_min variable establishes a minimum density below which D is set to D1, and above which the B-dependent viscosity is applied.

Warpy constructor: warpy.apps.mhd.viscousmhd.viscousmhd.bdependent_diffusivity_flux

Public Member Functions
	BdependentDiffusivityFlux ()

	~BdependentDiffusivityFlux () override

void	setup (const WxCryptSet &wxc) override

const std::vector< int > &	getInputVariableIndexes (int flag) const override

const std::vector< int > &	getAuxiliaryVariableIndexes (int flag) const override

const std::vector< int > &	getOutputVariableIndexes (int flag) const override

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

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

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

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

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
real	_gas_gamma
	Adiabatic Index.

real	_charge
	Charge of species.

real	_mass
	Mass of species.

real	_B_ref
	Reference magnetic field for B-dependent diffusivities.

real	_n_min
	Minimum density for B-dependent diffusivities.

real	_D_min
	Minimum diffusivity for B-dependent diffusivities.

real	_D_mom0
	Momentum diffusivity coefficient for B=0.

real	_D_therm0
	Thermal diffusivity coefficient for B=0.

real	_min_density
	Density floor.

real	_min_pressure
	Pressure floor.

real	_cfl_diff

std::string	_gradient_method

std::string	_coordinate_system

int	_radial_index

int	_ir

int	_ith

int	_iz

std::vector< int >	_input_variables

std::vector< int >	_aux_variables

std::vector< int >	_output_variables

std::vector< std::vector< real > >	_flux_tensor

Protected Attributes inherited from WmApplication
std::string	_app_name

WxLogStream	_debStrm

std::vector< int >	_allowedFlags

std::vector< std::string >	_onBoundaries

Additional Inherited Members
Public Types inherited from WmApplication
typedef Application_Variable	WmApplication_Variable

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

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

Constructor & Destructor Documentation

◆ BdependentDiffusivityFlux()

wxm::apps::viscousmhd::BdependentDiffusivityFlux::BdependentDiffusivityFlux ( )

◆ ~BdependentDiffusivityFlux()

wxm::apps::viscousmhd::BdependentDiffusivityFlux::~BdependentDiffusivityFlux ( )

override

Member Function Documentation

◆ getAuxiliaryVariableIndexes()

const std::vector< int > & wxm::apps::viscousmhd::BdependentDiffusivityFlux::getAuxiliaryVariableIndexes ( int flag ) const

inlineoverridevirtual

Reimplemented from WmApplication.

◆ getInputVariableIndexes()

const std::vector< int > & wxm::apps::viscousmhd::BdependentDiffusivityFlux::getInputVariableIndexes ( int flag ) const

inlineoverridevirtual

Reimplemented from wxm::app_base.

◆ getOutputVariableIndexes()

const std::vector< int > & wxm::apps::viscousmhd::BdependentDiffusivityFlux::getOutputVariableIndexes ( int flag ) const

inlineoverridevirtual

Reimplemented from wxm::app_base.

◆ internal_flux()

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

overridevirtual

Reimplemented from WmApplication.

◆ numerical_flux()

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::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

Reimplemented from WmApplication.

◆ numerical_flux_ip()

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::numerical_flux_ip	(	const real *	q_l,
		const real *	q_r,
		const real *	aux_l,
		const real *	aux_r,
		const solverVariables_t *	pFV,
		real *	numericalFlux
	)		const

◆ numerical_flux_ldg()

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::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

◆ setup()

void wxm::apps::viscousmhd::BdependentDiffusivityFlux::setup ( const WxCryptSet & wxc )

overridevirtual

Reimplemented from WmApplication.

Member Data Documentation

◆ _aux_variables

std::vector<int> wxm::apps::viscousmhd::BdependentDiffusivityFlux::_aux_variables

protected

◆ _B_ref

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_B_ref

protected

Reference magnetic field for B-dependent diffusivities.

◆ _cfl_diff

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_cfl_diff

protected

◆ _charge

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_charge

protected

Charge of species.

◆ _coordinate_system

std::string wxm::apps::viscousmhd::BdependentDiffusivityFlux::_coordinate_system

protected

◆ _D_min

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_D_min

protected

Minimum diffusivity for B-dependent diffusivities.

◆ _D_mom0

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_D_mom0

protected

Momentum diffusivity coefficient for B=0.

◆ _D_therm0

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_D_therm0

protected

Thermal diffusivity coefficient for B=0.

◆ _flux_tensor

std::vector<std::vector<real> > wxm::apps::viscousmhd::BdependentDiffusivityFlux::_flux_tensor

mutableprotected

◆ _gas_gamma

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_gas_gamma

protected

Adiabatic Index.

◆ _gradient_method

std::string wxm::apps::viscousmhd::BdependentDiffusivityFlux::_gradient_method

protected

◆ _input_variables

std::vector<int> wxm::apps::viscousmhd::BdependentDiffusivityFlux::_input_variables

protected

◆ _ir

int wxm::apps::viscousmhd::BdependentDiffusivityFlux::_ir

protected

◆ _ith

int wxm::apps::viscousmhd::BdependentDiffusivityFlux::_ith

protected

◆ _iz

int wxm::apps::viscousmhd::BdependentDiffusivityFlux::_iz

protected

◆ _mass

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_mass

protected

Mass of species.

◆ _min_density

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_min_density

protected

Density floor.

◆ _min_pressure

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_min_pressure

protected

Pressure floor.

◆ _n_min

real wxm::apps::viscousmhd::BdependentDiffusivityFlux::_n_min

protected

Minimum density for B-dependent diffusivities.

◆ _output_variables

std::vector<int> wxm::apps::viscousmhd::BdependentDiffusivityFlux::_output_variables

protected

◆ _radial_index

int wxm::apps::viscousmhd::BdependentDiffusivityFlux::_radial_index

protected

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

src/apps/mhd/viscousmhd/bdependent_diffusivity_flux.h

Detailed Description

Public Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ BdependentDiffusivityFlux()

◆ ~BdependentDiffusivityFlux()

Member Function Documentation

◆ getAuxiliaryVariableIndexes()

◆ getInputVariableIndexes()

◆ getOutputVariableIndexes()

◆ internal_flux()

◆ numerical_flux()

◆ numerical_flux_ip()

◆ numerical_flux_ldg()

◆ setup()

Member Data Documentation

◆ _aux_variables

◆ _B_ref

◆ _cfl_diff

◆ _charge

◆ _coordinate_system

◆ _D_min

◆ _D_mom0

◆ _D_therm0

◆ _flux_tensor

◆ _gas_gamma

◆ _gradient_method

◆ _input_variables

◆ _ir

◆ _ith

◆ _iz

◆ _mass

◆ _min_density

◆ _min_pressure

◆ _n_min

◆ _output_variables

◆ _radial_index