wxm::apps::mhd_two_temperature Namespace Reference

Namespaces
namespace	bc
namespace	hallmhd
namespace	imhd
namespace	limiters
namespace	radiation
namespace	resistive_mhd
namespace	viscousmhd

Classes
class	AppSetupHelper
	Helper class that automates common setup tasks for mhd physics applications. More...

Functions
real	getRhoFloored (const real *q, const real rho_min=std::numeric_limits< real >::epsilon())
	Get the floored mass density.
real	getIonNumberDensity (const real *q, const real Ai, const real rho_min=std::numeric_limits< real >::epsilon())
	Get the floored ion number density,.
real	getIonPressureFloored (const real *q, const real gas_gamma, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Get the ion pressure from MHD variables using floors for pressure and density.
real	getElectronPressureFloored (const real *q, const real gas_gamma, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Get the electron pressure from MHD variables using floors for pressure and density.
real	getFluidPressure (const real press_i, const real press_e)
	Get the the total fluid pressure from ion and electron pressures.
void	getGradientElectronPressure (const real *grad_q, const real gas_gamma, real *grad_pe)
	Get the gradient of electron pressure from MHD gradient variables.
void	getGradientIonPressure (const real *q, const real *grad_q, const real gas_gamma, real *grad_press_i, const real rho_min=std::numeric_limits< real >::epsilon())
	Get the gradient of ion pressure from MHD gradient variables.
real	getElectronTemperatureFloored (const real *q, const real gas_gamma, const real Ai, const real Zi, const real rho_min, const real press_min)
	Get the electron temperature from MHD gradient variables.
real	getIonTemperatureFloored (const real *q, const real gas_gamma, const real Ai, const real rho_min, const real press_min)
	Get the ion temperature from MHD gradient variables.
void	getGradientIonTemperature (const real *q, const real *grad_q, const real gas_gamma, const real Ai, real *grad_Ti, const real rho_min, const real press_min)
	Get the gradient of ion temperature from MHD gradient variables.
void	getGradientElectronTemperature (const real *q, const real *grad_q, const real gas_gamma, const real Ai, const real Zi, real *grad_Te, const real rho_min, const real press_min)
	Get the gradient of electron temperature from MHD gradient variables.
real	current_density_cart (const real skin_depth_norm, const real *grad_B[3], real *J)
real	current_density_cyl (const real skin_depth_norm, const real r, const real *B, const real *grad_B[3], const int ir, const int ith, const int iz, real *J)

Function Documentation

current_density_cart()

real wxm::apps::mhd_two_temperature::current_density_cart	(	const real	skin_depth_norm,
		const real *	grad_B[3],
		real *	J
	)

current_density_cyl()

real wxm::apps::mhd_two_temperature::current_density_cyl	(	const real	skin_depth_norm,
		const real	r,
		const real *	B,
		const real *	grad_B[3],
		const int	ir,
		const int	ith,
		const int	iz,
		real *	J
	)

getElectronPressureFloored()

real wxm::apps::mhd_two_temperature::getElectronPressureFloored	(	const real *	q,
		const real	gas_gamma,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Get the electron pressure from MHD variables using floors for pressure and density.

The floored pressure is given as

\[ p_{e} = \max(p_{e}, p_{min}), \]

where

\[ p_{e} = (\gamma - 1) e_{e} \]

Parameters

q	The raw MHD variables.
gas_gamma	Ratio of specific heats.
rho_min	Normalized minimum mass density.
press_min	Normalized minimum pressure.

Returns

Pressure calculated assuming pressure and density floors.

getElectronTemperatureFloored()

real wxm::apps::mhd_two_temperature::getElectronTemperatureFloored	(	const real *	q,
		const real	gas_gamma,
		const real	Ai,
		const real	Zi,
		const real	rho_min,
		const real	press_min
	)

Get the electron temperature from MHD gradient variables.

The electron temperature is given as

\[ T_{e} = \frac{p_{e}}{Z_{i} n_{i}} \]

Parameters

grad_q	The raw MHD gradient variables.
gas_gamma	Ratio of specific heats.
Ai	Normalized ion mass.
Zi	Normalized ion charge.
rho_min	Normalized minimm mass density.
press_min	Normalized minimum pressure.

Returns

T_e The electron temperature.

getFluidPressure()

real wxm::apps::mhd_two_temperature::getFluidPressure	(	const real	press_i,
		const real	press_e
	)

Get the the total fluid pressure from ion and electron pressures.

The floored pressure is given as

\[ p = p_{i} + p_{e} \]

Parameters

press_i	Ion pressure
press_e	Electron pressure

Returns

total fluid pressure

getGradientElectronPressure()

void wxm::apps::mhd_two_temperature::getGradientElectronPressure	(	const real *	grad_q,
		const real	gas_gamma,
		real *	grad_pe
	)

Get the gradient of electron pressure from MHD gradient variables.

The gradient of electron pressure is given as

\[ \nabla p_{e} = (\gamma - 1) \nabla e_{e} \]

Parameters

grad_q	The raw MHD gradient variables.
gas_gamma	Ratio of specific heats.
press_e	The vector gradient of electron pressure to be calculated.

getGradientElectronTemperature()

void wxm::apps::mhd_two_temperature::getGradientElectronTemperature	(	const real *	q,
		const real *	grad_q,
		const real	gas_gamma,
		const real	Ai,
		const real	Zi,
		real *	grad_Te,
		const real	rho_min,
		const real	press_min
	)

Get the gradient of electron temperature from MHD gradient variables.

The gradient of electron temperature is given as

\[ \nabla T_{e} = \nabla \left[\left(\frac{p_{e}}{n_{e}}\right)\right] \]

Parameters

q	The raw MHD variables.
grad_q	The raw MHD gradient variables.
gas_gamma	Ratio of specific heats.
Ai	Normalized ion mass.
Zi	Normalized ion charge.
grad_Te	The vector gradient of ion temperature to be calculated.
rho_min	Normalized minimum mass density.
press_min	Normalized minimum mass density.

getGradientIonPressure()

void wxm::apps::mhd_two_temperature::getGradientIonPressure	(	const real *	q,
		const real *	grad_q,
		const real	gas_gamma,
		real *	grad_press_i,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

Get the gradient of ion pressure from MHD gradient variables.

The gradient of ion pressure is given as

\[ \nabla p_{i} = \nabla \left[\left(\gamma - 1\right)\left(e_{i} - \frac{1}{2}\frac{\left(\rho \boldsymbol{v}\right)^{2}}{\rho}\right)\right] \]

Parameters

q	The raw MHD variables.
grad_q	The raw MHD gradient variables.
gas_gamma	Ratio of specific heats.
press_i	The vector gradient of electron pressure to be calculated.
rho_min	Normalized minimum mass density.

getGradientIonTemperature()

void wxm::apps::mhd_two_temperature::getGradientIonTemperature	(	const real *	q,
		const real *	grad_q,
		const real	gas_gamma,
		const real	Ai,
		real *	grad_Ti,
		const real	rho_min,
		const real	press_min
	)

Get the gradient of ion temperature from MHD gradient variables.

The gradient of ion temperature is given as

\[ \nabla T_{i} = \nabla \left[\left(\frac{p_{i}}{n_{i}}\right)\right] \]

Parameters

q	The raw MHD variables.
grad_q	The raw MHD gradient variables.
gas_gamma	Ratio of specific heats.
Ai	Normalized ion mass.
grad_Ti	The vector gradient of ion temperature to be calculated.
rho_min	Normalized minimum mass density.
press_min	Normalized minimum mass density.

getIonNumberDensity()

real wxm::apps::mhd_two_temperature::getIonNumberDensity	(	const real *	q,
		const real	Ai,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

Get the floored ion number density,.

The floored ion number density density is given as

\[ \rho_{fl} = \max(\rho / Ai, \rho_{min} / Ai), \]

Assumes \( \rho_{min} > 0 \).

Parameters

q	The raw MHD variables.
Ai	Normalized ion mass.
rho_min	Normalized minimum mass density.

Returns

Floored mass density.

getIonPressureFloored()

real wxm::apps::mhd_two_temperature::getIonPressureFloored	(	const real *	q,
		const real	gas_gamma,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Get the ion pressure from MHD variables using floors for pressure and density.

The floored pressure is given as

\[ p_{i} = \max(p_{i}, p_{min}), \]

where

\[ p_{i} = (\gamma - 1) \left( e_{i} - \frac{1}{2} \max(\rho, \rho_{min}) v^2 \right) \]

Assumes \( \rho_{min}, \; p_{min} > 0 \).

Parameters

q	The raw MHD variables.
gas_gamma	Ratio of specific heats.
rho_min	Normalized minimum mass density.
press_min	Normalized minimum mass density.

Returns

Pressure calculated assuming pressure and density floors.

getIonTemperatureFloored()

real wxm::apps::mhd_two_temperature::getIonTemperatureFloored	(	const real *	q,
		const real	gas_gamma,
		const real	Ai,
		const real	rho_min,
		const real	press_min
	)

Get the ion temperature from MHD gradient variables.

The electron temperature is given as

\[ T_{i} = \frac{p_{i}}{n_{i}} \]

Parameters

grad_q	The raw MHD gradient variables.
gas_gamma	Ratio of specific heats.
Ai	Normalized ion mass.
rho_min	Normalized minimm mass density.
press_min	Normalized minimum pressure.

Returns

T_i The ion temperature.

getRhoFloored()

real wxm::apps::mhd_two_temperature::getRhoFloored	(	const real *	q,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

Get the floored mass density.

The floored mass density is given as

\[ \rho_{fl} = \max(\rho, \rho_{min}), \]

Assumes \( \rho_{min} > 0 \).

Parameters

q	The raw MHD variables.
rho_min	Normalized minimum mass density.

Returns

Floored mass density.