Class used to implement a genaral C n^alpha_n T^alpha_T radiative cooling de/dt = - C n^alpha_n T^alpha_T where alpha_n and alpha_T are exponents Normalizing this equation, you can work out, in normalized units (dropping tildes), you get de/dt = - C n T^4 if C0 = 1/tau n_0^(1 - alpha_n) T_0^(1-alpha_T) More...

#include <generalized_nT.h>

Inheritance diagram for wxm::apps::mhd::radiation::GeneralizednT:

Detailed Description

Class used to implement a genaral C n^alpha_n T^alpha_T radiative cooling de/dt = - C n^alpha_n T^alpha_T where alpha_n and alpha_T are exponents Normalizing this equation, you can work out, in normalized units (dropping tildes), you get de/dt = - C n T^4 if C0 = 1/tau n_0^(1 - alpha_n) T_0^(1-alpha_T)

A specific case that can be of blackbody radiative cooling, where alpha_n = 1 and alpha_T = 4 de/dt = - C n T^4 This can be related to a volumetric cooling rate defined in Mikellides MRNAS2011 de/dt = - a c rho chi_p T^4 Here: a = Stefan's constant, a = 4 sigma / c = 7.565767E-16 [J m^-3 K^-4] / kB^4 where kB = 1.380649E-23 J K^-1 to express a in units of [m^-3 J^-3] c = speed of light [m s^-1] rho = mass density [kg m^-3] chi_p = mean Planck opacity [m^2 kg^-1] such that photon mean-free-path is 1/chi_p T = temperature in [J] This gives units of [W m^-3] for de/dt Equating this formulation of de/dt = - C n T^4 for a chosen C C = a c rho chi_p / n * chosen_factor [J^-3 s^-1] This C constant is passed into this class and should be normalized (multiplied by T0_J^3 * tau)

One can also interpret C in terms of an inverse Boltzmann number where 1/B0 = eps_B * sigma * T_B^3 / (rho_B * cp_B * V_B) where eps_B, T_B, rho_B, cp_B and V_B are some Boltzmann reference surface emissivity, temperature, density, specific heat constant a pressure, and velocity. Then C = 1/B0 / (T0_J^3 / tau).

Another case is T/n radiative cooling, where alpha_n = -1 and alpha_T = 1 In this case C0 looks like 1/tau n_0^2, which in SI units would be m^-6 s^-1

Public Member Functions
	GeneralizednT ()

	~GeneralizednT () override

void	setup (const WxCryptSet &wxc) override

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

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

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

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	_constant
	Black body radiation constant, \(C = a c \rho \chi_p / n * \) chosen_factor [J^-3 s^-1].

real	_gas_gamma
	Ratio of specific heats.

real	_Ai
	Proton normalized ion mass.

real	_Zi
	Ion charge.

real	_alpha_n

real	_alpha_T

real	_min_density
	Normalized minimum mass density.

real	_min_pressure
	Normalized minimum pressure density.

std::vector< int >	_fluid_variable_idcs

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

◆ GeneralizednT()

wxm::apps::mhd::radiation::GeneralizednT::GeneralizednT ( )

◆ ~GeneralizednT()

wxm::apps::mhd::radiation::GeneralizednT::~GeneralizednT ( )

override

Member Function Documentation

◆ getInputVariableIndexes()

const std::vector< int > & wxm::apps::mhd::radiation::GeneralizednT::getInputVariableIndexes ( int flag ) const

inlineoverridevirtual

Reimplemented from wxm::app_base.

◆ getOutputVariableIndexes()

const std::vector< int > & wxm::apps::mhd::radiation::GeneralizednT::getOutputVariableIndexes ( int flag ) const

inlineoverridevirtual

Reimplemented from wxm::app_base.

◆ setup()

void wxm::apps::mhd::radiation::GeneralizednT::setup ( const WxCryptSet & wxc )

overridevirtual

Reimplemented from WmApplication.

◆ source()

real wxm::apps::mhd::radiation::GeneralizednT::source	(	const real *	q,
		const real *	aux,
		const elementGeometry_t *	pEG,
		real *	source
	)		const

overridevirtual

Reimplemented from WmApplication.

Member Data Documentation

◆ _Ai

real wxm::apps::mhd::radiation::GeneralizednT::_Ai

protected

Proton normalized ion mass.

◆ _alpha_n

real wxm::apps::mhd::radiation::GeneralizednT::_alpha_n

protected

◆ _alpha_T

real wxm::apps::mhd::radiation::GeneralizednT::_alpha_T

protected

◆ _constant

real wxm::apps::mhd::radiation::GeneralizednT::_constant

protected

Black body radiation constant, \(C = a c \rho \chi_p / n * \) chosen_factor [J^-3 s^-1].

◆ _fluid_variable_idcs

std::vector<int> wxm::apps::mhd::radiation::GeneralizednT::_fluid_variable_idcs

protected

◆ _gas_gamma

real wxm::apps::mhd::radiation::GeneralizednT::_gas_gamma

protected

Ratio of specific heats.

◆ _min_density

real wxm::apps::mhd::radiation::GeneralizednT::_min_density

protected

Normalized minimum mass density.

◆ _min_pressure

real wxm::apps::mhd::radiation::GeneralizednT::_min_pressure

protected

Normalized minimum pressure density.

◆ _Zi

real wxm::apps::mhd::radiation::GeneralizednT::_Zi

protected

Ion charge.

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

src/apps/mhd/radiation/generalized_nT.h

Detailed Description

Public Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ GeneralizednT()

◆ ~GeneralizednT()

Member Function Documentation

◆ getInputVariableIndexes()

◆ getOutputVariableIndexes()

◆ setup()

◆ source()

Member Data Documentation

◆ _Ai

◆ _alpha_n

◆ _alpha_T

◆ _constant

◆ _fluid_variable_idcs

◆ _gas_gamma

◆ _min_density

◆ _min_pressure

◆ _Zi