Class to set gradient variables for conducting wall for Hall MHD. More...

#include <conducting_wall_freeslip_gradients_bc.h>

Inheritance diagram for wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients:

Detailed Description

Class to set gradient variables for conducting wall for Hall MHD.

See also: Latex Documentation: MHD BC File; Warpy constructor: warpy.apps.mhd.hallmhd.hallmhd.conducting_wall_freeslip_gradients

Conducting Wall applies:

\begin{align*} \boldsymbol{\hat{n}} \cdot \boldsymbol{B} =& 0 \end{align*}

\begin{align*} \boldsymbol{\hat{n}} \cdot \boldsymbol{v} =& 0 \end{align*}

\begin{align*} \boldsymbol{\hat{n}} \times \boldsymbol{E} =& 0 \end{align*}

where

\begin{align} \boldsymbol{E} =& -\boldsymbol{v}\times\boldsymbol{B} + \frac{1}{n_{\mathrm{e}}}\left(\boldsymbol{j}\times\boldsymbol{B} - \frac{1}{\left(\omega_{c}\tau\right)}\nabla p_{\mathrm{e}}\right) + \frac{\left(\nu_{p}\tau\right)}{\left(\omega_{c}\tau\right)}\eta\boldsymbol{j} \end{align}

This leads to a condition on the tangential components of \(\boldsymbol{j}\). If we assume we are in the frame of the wall, where \(\boldsymbol{\hat{n}} = \boldsymbol{\hat{x}}\), and \(\theta \equiv \frac{p_\mathrm{e}}{p_\mathrm{i}} \rightarrow \frac{p_\mathrm{e}}{p} = \frac{\theta}{\left(\theta + 1\right)} \), this leads to

\begin{align*} j_{y} =& \frac{\left(\omega_{c}\tau\right)}{\left(\nu_{p}\tau\right)}\frac{B_{z}}{n_{\mathrm{e}}\eta}j_{x} + \frac{1}{n_{\mathrm{e}}\eta\left(\nu_{p}\tau\right)}\frac{\theta}{\left(\theta + 1\right)} \left(\nabla p\right)_{y} \end{align*}

\begin{align*} j_{z} =& -\frac{\left(\omega_{c}\tau\right)}{\left(\nu_{p}\tau\right)}\frac{B_{y}}{n_{\mathrm{e}}\eta}j_{x} + \frac{1}{n_{\mathrm{e}}\eta\left(\nu_{p}\tau\right)}\frac{\theta}{\left(\theta + 1\right)} \left(\nabla p\right)_{z} \end{align*}

Public Member Functions
	ConductingWallFreeslipGradients ()

	~ConductingWallFreeslipGradients () 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

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

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

real	_skin_depth_norm

real	_Zi

real	_Ai

real	_theta

std::vector< int >	_var_idcs

std::vector< int >	_aux_var_idcs

real	_min_density_floor

real	_min_pressure_floor

std::string	_coordinate_system

int	_radial_index

int	_ir
	r index

int	_ith
	theta index

int	_iz
	z index

std::string	_resistivity_type

real	_max_eta

real	_min_eta

real	_n_vac

real	_eta_vac

real	_constant_resistivity_eta

bool	_const_resistivity

real	_omega_p_norm

real	_lnlam

real	_nu_p_norm

real	_Ae_hall

real	_Ze
	< Electron mass for Hall MHD model

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

◆ ConductingWallFreeslipGradients()

wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::ConductingWallFreeslipGradients ( )

◆ ~ConductingWallFreeslipGradients()

wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::~ConductingWallFreeslipGradients ( )

override

Member Function Documentation

◆ bc_q()

void wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::bc_q	(	const real *	q_in,
		const real *	aux_in,
		const real *	aux_out,
		const solverVariables_t *	pFV,
		real *	q_out
	)		const

overridevirtual

Boundary Condition Application which sets the boundary condition on ghost nodes.

Parameters

q_in	is the q variable vector on the inside (or "internal", "interior", "left", "minus", etc.) face node of the interface on which the boundary condition is set - this is an input
aux_in	is the aux variable vector on the inside (or "internal", "interior", "left", "minus", etc.) face node of the interface on which the boundary condition is set - this is an input
aux_out	is the aux variable vector on the outside (or "external", "exterior", "right", "plus", etc.) face node (a.k.a ghost node) of the interface on which the boundary condition is set - this is an input
q_out	is the q variable vector on the outside (or "external", "exterior", "right", "plus", etc.) face node (a.k.a ghost node) of the interface on which the boundary condition is set - this is an output - this is waht is being set

NOTE: If the boundary condition is virtual - the in and out nodes actually becomes the same: Thus q_in and q_out as well as aux_in and aux_out are actually the same internal node of the virtual subdomain. See dfem/variable_adjusters/boundary_conditions/boundary_condition.cc

Reimplemented from WmApplication.

◆ getAuxiliaryVariableIndexes()

const std::vector< int > & wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::getAuxiliaryVariableIndexes ( int flag ) const

inlineoverridevirtual

Reimplemented from WmApplication.

◆ getInputVariableIndexes()

const std::vector< int > & wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::getInputVariableIndexes ( int flag ) const

inlineoverridevirtual

Reimplemented from wxm::app_base.

◆ getOutputVariableIndexes()

const std::vector< int > & wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::getOutputVariableIndexes ( int flag ) const

inlineoverridevirtual

Reimplemented from wxm::app_base.

◆ setup()

void wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::setup ( const WxCryptSet & wxc )

overridevirtual

Reimplemented from WmApplication.

Member Data Documentation

◆ _Ae_hall

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_Ae_hall

protected

◆ _Ai

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_Ai

protected

◆ _aux_var_idcs

std::vector<int> wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_aux_var_idcs

protected

◆ _const_resistivity

bool wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_const_resistivity

protected

◆ _constant_resistivity_eta

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_constant_resistivity_eta

protected

◆ _coordinate_system

std::string wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_coordinate_system

protected

◆ _eta_vac

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_eta_vac

protected

◆ _gas_gamma

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_gas_gamma

protected

◆ _ir

int wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_ir

protected

r index

◆ _ith

int wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_ith

protected

theta index

◆ _iz

int wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_iz

protected

z index

◆ _lnlam

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_lnlam

protected

◆ _max_eta

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_max_eta

protected

◆ _min_density_floor

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_min_density_floor

protected

◆ _min_eta

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_min_eta

protected

◆ _min_pressure_floor

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_min_pressure_floor

protected

◆ _n_vac

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_n_vac

protected

◆ _nu_p_norm

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_nu_p_norm

protected

◆ _omega_p_norm

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_omega_p_norm

protected

◆ _radial_index

int wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_radial_index

protected

◆ _resistivity_type

std::string wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_resistivity_type

protected

◆ _skin_depth_norm

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_skin_depth_norm

protected

◆ _theta

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_theta

protected

◆ _var_idcs

std::vector<int> wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_var_idcs

protected

◆ _Ze

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_Ze

protected

< Electron mass for Hall MHD model

◆ _Zi

real wxm::apps::hallmhd::bc::ConductingWallFreeslipGradients::_Zi

protected

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

src/apps/mhd/hallmhd/conducting_wall_freeslip_gradients_bc.h

Detailed Description

Public Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ ConductingWallFreeslipGradients()

◆ ~ConductingWallFreeslipGradients()

Member Function Documentation

◆ bc_q()

◆ getAuxiliaryVariableIndexes()

◆ getInputVariableIndexes()

◆ getOutputVariableIndexes()

◆ setup()

Member Data Documentation

◆ _Ae_hall

◆ _Ai

◆ _aux_var_idcs

◆ _const_resistivity

◆ _constant_resistivity_eta

◆ _coordinate_system

◆ _eta_vac

◆ _gas_gamma

◆ _ir

◆ _ith

◆ _iz

◆ _lnlam

◆ _max_eta

◆ _min_density_floor

◆ _min_eta

◆ _min_pressure_floor

◆ _n_vac

◆ _nu_p_norm

◆ _omega_p_norm

◆ _radial_index

◆ _resistivity_type

◆ _skin_depth_norm

◆ _theta

◆ _var_idcs

◆ _Ze

◆ _Zi