Bennett Equilibrium for Ideal MHD Should Work for Cylindrical and Cartesian cases Ref. More...

#include <bennett_equilibrium.h>

Inheritance diagram for wxm::apps::functions::mhd::BennettEquilibrium:

Detailed Description

Bennett Equilibrium for Ideal MHD Should Work for Cylindrical and Cartesian cases Ref.

Freidberg Rev. Mod. Phys. 1982 For momentum equilibrium: grad p = J x B For a Z-pinch configuration with B = B_theta(r) \hat(theta) J = J_z(r) \hat(z) This results in d/dr(p + Bth^2/(2mu0)) + Bth^2/(\mu0 r) = 0 where Jz = curl B / mu0 is used Bennett shows the following profiles satisfies this equilibrium: p = mu0 I^2 / (8 pi^2) * a^2 / (r^2 + a^2)^2 Jz = I/pi * a^2/(r^2 + a^2)^2 Bth = mu0 I / (2 pi) * r / (r^2 + a^2) where I = prescribed pinch current and a = prescribed pinch radius

We convert this to WARPXM units J = curl B / wct grad p = wct * J x B d/dr(p + Bth^2/2) + Bth^2/r = 0 p = wct^2 * I^2 / (8 pi^2) * a^2 / (r^2 + a^2)^2 Jz = I / pi * a^2 / (r^2 + a^2)^2 Bth = wct * I / (2 pi) * r / (r^2 + a^2) where wct = (omega_c tau)

We also assume uniform temperature, then rho = A * n = A * p / T

For warpy class see warpy.apps.functions.mhd.bennett_equilibrium

Public Member Functions
	BennettEquilibrium ()
	Constructor.

	~BennettEquilibrium () override
	Destructor.

void	setup (const WxCryptSet &wxc) override
	Setup.

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

void	evaluate_function (const real q, const real aux, const solverVariables_t pSV, real result) const override
	Redefinition of the function evaluator.

void	bc_q (const real q_in, const real aux_in, const real aux_out, const solverVariables_t pFV, real *q_out) const override
	Redefinition of the bc.

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 ()

Public Member Functions inherited from wxm::app_base
virtual const std::vector< int > &	getInputVariableIndexes (int flag=0) const

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

Protected Attributes
std::vector< int >	_mhd_fluid

std::string	_coordinate_system

int	_ir

int	_ith

int	_iz

real	_gas_gamma

real	_Ai

real	_Zi

real	_T

real	_a

real	_I

real	_wct

real	_pert

real	_lambda

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

◆ BennettEquilibrium()

wxm::apps::functions::mhd::BennettEquilibrium::BennettEquilibrium ( )

Constructor.

◆ ~BennettEquilibrium()

wxm::apps::functions::mhd::BennettEquilibrium::~BennettEquilibrium ( )

override

Destructor.

Member Function Documentation

◆ bc_q()

void wxm::apps::functions::mhd::BennettEquilibrium::bc_q	(	const real *	q_in,
		const real *	aux_in,
		const real *	aux_out,
		const solverVariables_t *	pFV,
		real *	q_out
	)		const

overridevirtual

Redefinition of the bc.

Parameters

const	q_in - input variable inside
const	aux_in - auxiliary variable inside
const	aux_out - auxiliary variable outside
const	pFV - solver variable structure
q_out	- output variable outside

Reimplemented from WmApplication.

◆ evaluate_function()

void wxm::apps::functions::mhd::BennettEquilibrium::evaluate_function	(	const real *	q,
		const real *	aux,
		const solverVariables_t *	pSV,
		real *	result
	)		const

overridevirtual

Redefinition of the function evaluator.

Parameters

const	q - input variable
const	aux - auxiliary variable
const	pSV - solver variable structure
result	- output variable

Reimplemented from WmApplication.

◆ getOutputVariableIndexes()

const std::vector< int > & wxm::apps::functions::mhd::BennettEquilibrium::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.

◆ setup()

void wxm::apps::functions::mhd::BennettEquilibrium::setup ( const WxCryptSet & wxc )

overridevirtual

Setup.

Parameters

WxCryptSet object

Reimplemented from WmApplication.

Member Data Documentation

◆ _a

real wxm::apps::functions::mhd::BennettEquilibrium::_a

protected

◆ _Ai

real wxm::apps::functions::mhd::BennettEquilibrium::_Ai

protected

◆ _coordinate_system

std::string wxm::apps::functions::mhd::BennettEquilibrium::_coordinate_system

protected

◆ _gas_gamma

real wxm::apps::functions::mhd::BennettEquilibrium::_gas_gamma

protected

◆ _I

real wxm::apps::functions::mhd::BennettEquilibrium::_I

protected

◆ _ir

int wxm::apps::functions::mhd::BennettEquilibrium::_ir

protected

◆ _ith

int wxm::apps::functions::mhd::BennettEquilibrium::_ith

protected

◆ _iz

int wxm::apps::functions::mhd::BennettEquilibrium::_iz

protected

◆ _lambda

real wxm::apps::functions::mhd::BennettEquilibrium::_lambda

protected

◆ _mhd_fluid

std::vector<int> wxm::apps::functions::mhd::BennettEquilibrium::_mhd_fluid

protected

◆ _pert

real wxm::apps::functions::mhd::BennettEquilibrium::_pert

protected

◆ _T

real wxm::apps::functions::mhd::BennettEquilibrium::_T

protected

◆ _wct

real wxm::apps::functions::mhd::BennettEquilibrium::_wct

protected

◆ _Zi

real wxm::apps::functions::mhd::BennettEquilibrium::_Zi

protected

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

src/apps/function_evaluators/mhd/bennett_equilibrium.h

Detailed Description

Public Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ BennettEquilibrium()

◆ ~BennettEquilibrium()

Member Function Documentation

◆ bc_q()

◆ evaluate_function()

◆ getOutputVariableIndexes()

◆ setup()

Member Data Documentation

◆ _a

◆ _Ai

◆ _coordinate_system

◆ _gas_gamma

◆ _I

◆ _ir

◆ _ith

◆ _iz

◆ _lambda

◆ _mhd_fluid

◆ _pert

◆ _T

◆ _wct

◆ _Zi