imhd.h File Reference

#include <cmath>
#include "warpxm/warpxm_config.h"
#include "apps/general_functions/geometry.h"

Go to the source code of this file.

Functions
real	max_wave_speed (const real gas_gamma, const real *q, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	max_wave_speed_magnitude (const real gas_gamma, const real *q, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	min_wave_speed (real gas_gamma, const real *q, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	calc_fast_magnetosonic (real gas_gamma, const real *q, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	calc_slow_magnetosonic (real gas_gamma, const real *q, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	calc_magnetosonic_speeds (const real gas_gamma, const real *q, real *c, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Calculate magnetosonic speeds in local frame, normal to element boundary.
real	rusanov_flux (const real gas_gamma, const real *ql, const real *qr, const real *F_L, const real *F_R, real *F_num, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	hll_flux (const real gas_gamma, const real *ql, const real *qr, const real *F_L, const real *F_R, real *F_num, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	hlld_flux (const real gas_gamma, const real *ql, const real *qr, const real *F_L, const real *F_R, real *F_num, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	get_avg (real a, real b)
real	get_delta_lambda_k (const real lambda_k_R, const real lambda_k_L)
real	get_lambda_k_star (const real lambda_k_roe, const real lambda_k_R, const real lambda_k_L)
real	roe_flux (const real gas_gamma, const real *ql, const real *qr, const real *F_L, const real *F_R, real *F_num, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	imhd_numerical_flux_local_frame (const real gas_gamma, const real *q, real *f, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	IMHD numerical flux vector calculated in frame rotated to element boundary.
real	imhd_numerical_flux (const real gas_gamma, const real *q_l, const real *q_r, const real *aux_l, const real *aux_r, const solverVariables_t *pFV, const std::string &flux_type, real *numericalFlux, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	IMHD numerical flux vector calculated in global frame.
void	imhd_internal_flux (const real gas_gamma, const solverVariables_t *pSV, const real *q, std::vector< std::vector< real > > &internalFlux, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	IMHD internal flux tensor calculated in global frame.
void	CtoNC_MHD (const real gas_gamma, const real QC[8], real QNC[8], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Converts conserved variables to nonconserved (primitive) variables.
void	NCtoC_MHD (const real gas_gamma, const real QNC[8], real QC[8], const real rho_min=std::numeric_limits< real >::epsilon())
	Converts nonconserved (primitive) variables to conserved variables.
void	dqdw_MHD (const real gas_gamma, const real Q[8], real dqdw[][8], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	dwdq_MHD (const real gas_gamma, const real Q[8], real dwdq[][8], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	conducting_wall_noslip (const real gas_gamma, const solverVariables_t *pFV, const real *QC, const real vx_w, const real vy_w, const real vz_w, real *QC_w, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	conducting_wall_noslip_old (const real gas_gamma, const solverVariables_t *pFV, const real *QC, const real vx_w, const real vy_w, const real vz_w, real *QC_w, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	conducting_wall_noslip_gradients (const real gas_gamma, const solverVariables_t *pFV, const real *QC, real *QC_w, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	conducting_wall_freeslip (const real gas_gamma, const solverVariables_t *pFV, const real *QC, real *QC_w, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	conducting_wall_freeslip_gradients (const real gas_gamma, const solverVariables_t *pFV, const real *QC, const real *aux_in, const real *aux_out, real *QC_w, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	twofluid_to_imhd (const real *QC, const solverVariables_t *pSV, real oc_sd, real *QC_w)
void	copyout (const real *QC, real *QC_w)
void	copyout_gradients (const real *grad_QC, real *grad_QC_w)
void	freeslipWallCondition_imhd (const real gas_gamma, const solverVariables_t *pFV, const real *QC, real *QC_w, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	applyLdgPenaltyEta (const solverVariables_t *pFV, const real *q_l, const real *q_r, real *numericalFlux)
	Apply LDG eta penalty to numerical flux.

Function Documentation

applyLdgPenaltyEta()

void applyLdgPenaltyEta	(	const solverVariables_t *	pFV,
		const real *	q_l,
		const real *	q_r,
		real *	numericalFlux
	)

Apply LDG eta penalty to numerical flux.

See Datta dissertation, Section 3.2 for construction of the LDG method as implemented here. The "eta" penalty-weighting parameter in the code is refered to as "alpha" in the dissertation, and the stabalizing penalty "tau" in Hesthaven "Nodal Discontinuous Galerkin Methods" 2008.

See Hesthaven, Chapter 7.2 for further reading on the topic, and the selection of values for eta/alpha/tau.

Parameters

const	solverVariables_t pFV - solver variable structure
const	real q_l - input variable, left
const	real q_r - input variable, right
real	numericalFlux - numerical fluxes

calc_fast_magnetosonic()

real calc_fast_magnetosonic	(	real	gas_gamma,
		const real *	q,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

calc_magnetosonic_speeds()

void calc_magnetosonic_speeds	(	const real	gas_gamma,
		const real *	q,
		real *	c,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Calculate magnetosonic speeds in local frame, normal to element boundary.

@warn Intended for use with numerical flux calcs. Looks for speeds normal to element boundary in local frame (x direction).

Parameters

gas_gamma	Adiabatic index.
q	Array of MHD variables.
c	Array of speeds.
rho_min	Minimum density.
press_min	Minimum pressure.

calc_slow_magnetosonic()

real calc_slow_magnetosonic	(	real	gas_gamma,
		const real *	q,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

conducting_wall_freeslip()

void conducting_wall_freeslip	(	const real	gas_gamma,
		const solverVariables_t *	pFV,
		const real *	QC,
		real *	QC_w,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

conducting_wall_freeslip_gradients()

void conducting_wall_freeslip_gradients	(	const real	gas_gamma,
		const solverVariables_t *	pFV,
		const real *	QC,
		const real *	aux_in,
		const real *	aux_out,
		real *	QC_w,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

conducting_wall_noslip()

void conducting_wall_noslip	(	const real	gas_gamma,
		const solverVariables_t *	pFV,
		const real *	QC,
		const real	vx_w,
		const real	vy_w,
		const real	vz_w,
		real *	QC_w,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

conducting_wall_noslip_gradients()

void conducting_wall_noslip_gradients	(	const real	gas_gamma,
		const solverVariables_t *	pFV,
		const real *	QC,
		real *	QC_w,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

conducting_wall_noslip_old()

void conducting_wall_noslip_old	(	const real	gas_gamma,
		const solverVariables_t *	pFV,
		const real *	QC,
		const real	vx_w,
		const real	vy_w,
		const real	vz_w,
		real *	QC_w,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

copyout()

void copyout	(	const real *	QC,
		real *	QC_w
	)

copyout_gradients()

void copyout_gradients	(	const real *	grad_QC,
		real *	grad_QC_w
	)

CtoNC_MHD()

void CtoNC_MHD	(	const real	gas_gamma,
		const real	QC[8],
		real	QNC[8],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Converts conserved variables to nonconserved (primitive) variables.

Parameters

QC	Resultant conserved variables
QNC	Nonconserved variables
rho_min	Minimum density.
press_min	Minimum pressure.

dqdw_MHD()

void dqdw_MHD	(	const real	gas_gamma,
		const real	Q[8],
		real	dqdw[][8],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

dwdq_MHD()

void dwdq_MHD	(	const real	gas_gamma,
		const real	Q[8],
		real	dwdq[][8],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

freeslipWallCondition_imhd()

void freeslipWallCondition_imhd	(	const real	gas_gamma,
		const solverVariables_t *	pFV,
		const real *	QC,
		real *	QC_w,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

get_avg()

real get_avg	(	real	a,
		real	b
	)

get_delta_lambda_k()

real get_delta_lambda_k	(	const real	lambda_k_R,
		const real	lambda_k_L
	)

get_lambda_k_star()

real get_lambda_k_star	(	const real	lambda_k_roe,
		const real	lambda_k_R,
		const real	lambda_k_L
	)

hll_flux()

real hll_flux	(	const real	gas_gamma,
		const real *	ql,
		const real *	qr,
		const real *	F_L,
		const real *	F_R,
		real *	F_num,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

hlld_flux()

real hlld_flux	(	const real	gas_gamma,
		const real *	ql,
		const real *	qr,
		const real *	F_L,
		const real *	F_R,
		real *	F_num,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

imhd_internal_flux()

void imhd_internal_flux	(	const real	gas_gamma,
		const solverVariables_t *	pSV,
		const real *	q,
		std::vector< std::vector< real > > &	internalFlux,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

IMHD internal flux tensor calculated in global frame.

See also

MHD writeup document

Parameters

pC	IMHD constant struct.
q	Vector of MHD variables.
pFV	Solver variable struct. Holds element and node geometry info(?).
internalFlux	Rank two tensor of IMHD internal fluxes being returned.
rho_min	Minimum density.
press_min	Minimum pressure.

imhd_numerical_flux()

real imhd_numerical_flux	(	const real	gas_gamma,
		const real *	q_l,
		const real *	q_r,
		const real *	aux_l,
		const real *	aux_r,
		const solverVariables_t *	pFV,
		const std::string &	flux_type,
		real *	numericalFlux,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

IMHD numerical flux vector calculated in global frame.

See also

MHD writeup document

Procedure for calculating the numerical flux

1. Rotate vector into element face frame.
2. Calculate flux in face frame for left and right variables.
3. Calculate numerical flux.
4. Rotate back to global frame.
5. Assign numerical fluxes to numericalFlux.

Parameters

pC	IMHD constant struct.
q_l	Vector of MHD variables on left of element boundary.
q_r	Vector of MHD variable on right of element boundary.
aux_l	NOT USED.
aux_r	NOT USED.
pFV	Solver variable struct. Holds element and node geometry info(?).
flux_type	String with name of numerical flux type.
numericalFlux	Vector of IMHD numerical fluxes being returned.
rho_min	Minimum density.
press_min	Minimum pressure.

imhd_numerical_flux_local_frame()

void imhd_numerical_flux_local_frame	(	const real	gas_gamma,
		const real *	q,
		real *	f,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

IMHD numerical flux vector calculated in frame rotated to element boundary.

In the rotated frame, x is normal to the boundary and y and z are tangential.

Ideal MHD rotated flux vector:

\begin{align} \overline{\mathcal{F}}_x=\begin{bmatrix} \rho u \\ \rho u u - (B_xB_x - \frac{1}{2}B^2) + P \\ \rho u v - B_xB_y \\ \rho u w - B_xB_z \\ u(\varepsilon+P + \frac{1}{2}B^2) - (\boldsymbol{u} \cdot \boldsymbol{B}) B_x \\ 0 \\ u B_y - B_x v \\ u B_z - B_x w \end{bmatrix} \end{align}

See also

MHD writeup document

Parameters

gas_gamma	Ratio of specific heats.
q	IMHD fluid variables rotated into the element surface frame.
f	Vector of IMHD numerical fluxes.
rho_min	Minimum density.
press_min	Minimum pressure.

max_wave_speed()

real max_wave_speed	(	const real	gas_gamma,
		const real *	q,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

max_wave_speed_magnitude()

real max_wave_speed_magnitude	(	const real	gas_gamma,
		const real *	q,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

min_wave_speed()

real min_wave_speed	(	real	gas_gamma,
		const real *	q,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

NCtoC_MHD()

void NCtoC_MHD	(	const real	gas_gamma,
		const real	QNC[8],
		real	QC[8],
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

Converts nonconserved (primitive) variables to conserved variables.

Parameters

QNC	Nonconserved variables
QC	Resultant conserved variables
rho_min	Minimum density.

roe_flux()

real roe_flux	(	const real	gas_gamma,
		const real *	ql,
		const real *	qr,
		const real *	F_L,
		const real *	F_R,
		real *	F_num,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

rusanov_flux()

real rusanov_flux	(	const real	gas_gamma,
		const real *	ql,
		const real *	qr,
		const real *	F_L,
		const real *	F_R,
		real *	F_num,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

twofluid_to_imhd()

void twofluid_to_imhd	(	const real *	QC,
		const solverVariables_t *	pSV,
		real	oc_sd,
		real *	QC_w
	)