wxm::apps::rmhd Namespace Reference

Namespaces
namespace	bc

Classes
class	CurrentDensity
	Class that calculates the current gradient J from deritives of B: That is, J = skin_depth_norm * curl(B) More...
class	CylSource
	Implements the source terms in the resistitive diffusion terms that are added to Ideal MHD to produce the resistive MHD equations arising from a cylindrical geometry. More...
class	DensityDiffusionCylSource
	Cylindrical source for density diffusion in the MHD model. More...
class	DensityDiffusionFlux
	Density diffusion flux for the MHD model. More...
class	ElectricField
	Class that calculates the electric field from Ohm's Law using ideal and resistive terms E = -u x B + (dp/L) * (nupt) * eta * J. More...
class	ohmic_source_t
	class that calculates a source associated with reduced Ohmic heating More...
class	WmApplication_Resistive_Diffusion

Functions
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)
real	get_eta (const real *q, const real J[3], const bool const_resistivity, const real constant_resistivity_eta, const std::string resistivity_type, const real max_eta, const real min_eta, const real n_vac, const real eta_vac, const real gas_gamma, const real ompt, const real nupt, const real lnlam=10.0, const real Ai=1.0, const real Zi=1.0, const real Ae=1.0/1836.0, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	get_resistivity (const real *q, const real gas_gamma, const real lnlam=10, const real Ai=1.0, const real Zi=1.0, const real Ae=1.0/1836.0, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Compute Spitzer-like resistivity.
real	get_resistivity_chodura (const real *q, const real J[3], const real gas_gamma, const real ompt, const real nupt, const real lnlam=10, const real Ai=1.0, const real Zi=1.0, const real Ae=1.0/1836.0, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Compute Chodura resistivity.
real	rmhd_internal_diffusion_flux (const real nu_p_norm, const real skin_depth_norm, const solverVariables_t *pSV, const real *q, const real *J, const real eta, std::vector< std::vector< real > > &internal_diffusion_flux)
void	noslipWallCondition_MHD (const real gas_gamma, const solverVariables_t *pSV, const real *QC, const real vx_w, const real vy_w, const real vz_w, const real bx_w, const real by_w, const real bz_w, real *QC_w, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	set_time_step (const solverVariables_t *pSV, const real j_coefficient, const real diffusion_coefficient, const real eta, const real cfl_diff=0.5)
	Suggested time step calculation for RMHD resistive diffusion.

Function Documentation

current_density_cart()

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

current_density_cyl()

real wxm::apps::rmhd::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
	)

get_eta()

real wxm::apps::rmhd::get_eta	(	const real *	q,
		const real	J[3],
		const bool	const_resistivity,
		const real	constant_resistivity_eta,
		const std::string	resistivity_type,
		const real	max_eta,
		const real	min_eta,
		const real	n_vac,
		const real	eta_vac,
		const real	gas_gamma,
		const real	ompt,
		const real	nupt,
		const real	lnlam = 10.0,
		const real	Ai = 1.0,
		const real	Zi = 1.0,
		const real	Ae = 1.0/1836.0,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

get_resistivity()

real wxm::apps::rmhd::get_resistivity	(	const real *	q,
		const real	gas_gamma,
		const real	lnlam = 10,
		const real	Ai = 1.0,
		const real	Zi = 1.0,
		const real	Ae = 1.0/1836.0,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Compute Spitzer-like resistivity.

Compute Spitzer-like resistivity [Goldston and Rutherford IoP (1995), Eq. 11.29] note that for parallel resistivity, this is ~2x too large; see [G&R Eq. 11.31 and associated discussion]

The normalized eta is (see Datta dissertation Appx. A (Eq. A.2.1) for normalization):

\[ \eta = \sqrt{2} Z_i \ln(\lambda) A_e^{0.5} T_e^{-1.5} \]

Warning

Users should be careful that their chosen normalization is consistent with the normalization in Datta dissertation Appx. A (Eq. A.2.1). For example, if the electron mass is not 1/1836, this resistivity calculation will not be consistent with that choice.

Parameters

q	The raw MHD variables.
gas_gamma	Ratio of specific heats.
lnlam	Coulomb logarithm.
Ai	Proton normalized ion mass.
Zi	Ion charge.
Ae	Proton normalized electron mass.
rho_min	Normalized minimum mass density.
press_min	Normalized minimum mass density.

Returns

Spitzer resistivity eta.

get_resistivity_chodura()

real wxm::apps::rmhd::get_resistivity_chodura	(	const real *	q,
		const real	J[3],
		const real	gas_gamma,
		const real	ompt,
		const real	nupt,
		const real	lnlam = 10,
		const real	Ai = 1.0,
		const real	Zi = 1.0,
		const real	Ae = 1.0/1836.0,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Compute Chodura resistivity.

Compute Chodura resistivity [Sgro and Nielson, Phys. Fluids 1976].

Warning

Users should be careful that their chosen normalization is consistent with the normalization in Datta dissertation Appx. A (Eq. A.2.1). For example, if the electron mass is not 1/1836, this resistivity calculation will not be consistent with that choice.

Parameters

q	The raw MHD variables.
J	Current density.
gas_gamma	Ratio of specific heats.
ompt	Normalized proton plasma frequency.
nupt	Normalized proton-proton collision frequency.
lnlam	Coulomb logarithm.
Ai	Proton normalized ion mass.
Zi	Ion charge.
Ae	Proton normalized electron mass.
rho_min	Normalized minimum mass density.

Returns

Pressure calculated assuming pressure and density floors.

noslipWallCondition_MHD()

void wxm::apps::rmhd::noslipWallCondition_MHD	(	const real	gas_gamma,
		const solverVariables_t *	pSV,
		const real *	QC,
		const real	vx_w,
		const real	vy_w,
		const real	vz_w,
		const real	bx_w,
		const real	by_w,
		const real	bz_w,
		real *	QC_w,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

rmhd_internal_diffusion_flux()

real wxm::apps::rmhd::rmhd_internal_diffusion_flux	(	const real	nu_p_norm,
		const real	skin_depth_norm,
		const solverVariables_t *	pSV,
		const real *	q,
		const real *	J,
		const real	eta,
		std::vector< std::vector< real > > &	internal_diffusion_flux
	)

set_time_step()

real wxm::apps::rmhd::set_time_step	(	const solverVariables_t *	pSV,
		const real	j_coefficient,
		const real	diffusion_coefficient,
		const real	eta,
		const real	cfl_diff = 0.5
	)

Suggested time step calculation for RMHD resistive diffusion.

dB/dt + curl [ nuptau * (dp/L)^2 * eta * curl B ] = 0 j_coefficient = dp/L diffusion_coefficient = nuptau * (dp/L)

for diffusive time step limit:

• dt_max = cfl_diff dx_eff^2 / D
• let dx_eff = cfl*dx, where cfl is the warpxm-style cfl (which takes into account the spatial order), and dx is the element size
• thus, dt_max = cfl^2*dx^2 / D

Parameters

pSV	Struct of elemenent geometry related information.
j_coefficient	dp/L
diffusion_coefficient	nuptau * (dp/L)
eta	Resistivity.
cfl_diff	Coefficient on the CFL for diffusion. Default 0.5.

Returns

Suggested maximum time step.