wxm::apps::five_moment Namespace Reference

Namespaces
namespace	bc
namespace	limiters

Classes
class	AppSetupHelper
	Helper class that automates common setup tasks for 5-moment fluid physics applications. More...
class	braginskii_flux
class	ConservedPrimitiveConversion
class	DensityDiffusionCylSource
class	DensityDiffusionFlux
class	Euler
	Euler flux. More...
class	Euler1D_Riemann_Problem_Analytic_Solution
	Class that calculates the analytic solution to the Riemann Problem for the Euler Equations. More...
class	EulerCylSource
	Implements the source terms in the Euler equations arising from a cylindrical geometry. More...
class	FieldSource
class	five_moment_to_kinetic
	5-Moment to Kinetic Boundary Condition App More...
class	GeneralSource
class	InterspeciesCollisions
class	IntraspeciesCollisions
	Implements Navier-Stokes style collisions. More...
class	IntraspeciesCyl
	Implements the source terms for intraspecies collisions arising from a cylindrical geometry. More...
class	NavierStokes
class	ReactionSource
	Implements source terms for atomic reactions. More...
class	ReactionSourceMol

Functions
real	getRhoFloored (const real *q, const real rho_min=std::numeric_limits< real >::epsilon())
	Get the floored mass density.
real	getPressureFloored (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 pressure from Euler (5-moment) variables using floors for pressure and density.
real	getTemperatureFloored (const real *q, const real gas_gamma, const real A=1.0, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Get the temperature from Euler (5-moment) variables using floors for pressure and density.
void	NCtoC (const constants_5moment_t *pC, const real QNC[5], real QC[5])
	Converts nonconserved (primitive) variables to conserved variables.
void	CtoNC (const constants_5moment_t *pC, const real QC[5], real QNC[5], 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	NCtoCDifferential (const constants_5moment_t *pC, const real QNC_center[5], const real dQNC[5], const real QC_center[5], real dQC[5])
	This currently isn't used anywhere.
void	rotateVector (const real v[5], const solverVariables_t *pSV, real Rv[5])
	Rotates a 5-moment variable set from world frame to local frame.
void	antirotateVector (const real Rv[5], const solverVariables_t *pSV, real v[5])
	Rotates a 5-moment variable set from local frame to world frame.
void	eulerFlux (const constants_5moment_t *pC, const real QC[5], real flux[5], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Flux along x-axis for Euler fluid equations using conserved variables.
void	eulerRoeFluxSolver (const constants_5moment_t *pC, const real QC_l[5], const real QC_r[5], real *s, real amdq[5], real apdq[5], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Solves the full Roe decomposition for the euler fluid problem using conserved variables - assumes an entropy fix - function is stolen from WARPX.
void	eulerRoeAverages (const constants_5moment_t *pC, const real ql[5], const real qr[5], const real &pl, const real &pr, real &rho, real &u, real &v, real &w, real &enth, real &a, const real rho_min=std::numeric_limits< real >::epsilon())
void	hartenHymanEntropyFix (const constants_5moment_t *pC, const real ql[5], const real qr[5], const real s[3], const real wave[][3], real amdq[5], real apdq[5], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	eulerNumericalFlux_x (const constants_5moment_t *pC, const real QC_l[5], const real QC_r[5], void(*numerical_flux_scheme)(const constants_5moment_t *pC, const real QC_l[5], const real QC_r[5], real *s, real amdq[5], real apdq[5], const real rho_min, const real press_min), real flux[5], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Calculates the Euler Numerical flux given a scheme along the x-axis which is to be used as a numerical flux.
real	eulerNumericalFlux (const constants_5moment_t *pC, const solverVariables_t *pSV, const real QC_l[5], const real QC_r[5], void(*numerical_flux_scheme)(const constants_5moment_t *pC, const real QC_l[5], const real QC_r[5], real *s, real amdq[5], real apdq[5], const real rho_min, const real press_min), real numericalFlux[5], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Calculates the Numerical Flux for the Euler fluid equations using Roe's Method as given by Leveque in "Finite Volume Methods for Hyperbolic Problems" equation 15.40 for a given numerical Flux scheme (Roe, HLLE, etc.)
void	eulerHLLEFluxSolver (const constants_5moment_t *pC, const real QC_l[5], const real QC_r[5], real *s, real amdq[5], real apdq[5], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Calculates the HLLE flux for the Euler fluid equations.
void	eulerHLLECFluxSolver (const constants_5moment_t *pC, const real QC_l[5], const real QC_r[5], real *s, real amdq[5], real apdq[5], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	eulerRusanovFlux (const constants_5moment_t *pC, const solverVariables_t *pSV, const real QC_l[5], const real QC_r[5], real numericalFlux[5], const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Calculates the Rusanov flux for the Euler fluid equations directly.
real	eulerInternalFlux (const constants_5moment_t *pC, const solverVariables_t *pSV, const real QC[5], std::vector< std::vector< real > > &internalFlux, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Calculates the internal euler flux at a given point.
void	navier_stokes_anisotropic_pressure_tensor (const real viscosity, const real *q, const real *grad_rho, const real *grad_p[3], real pi[3][3])
void	navier_stokes_viscous_flux_tensor (const real *q, const solverVariables_t *pSV, const real pi[][3], const real h[3], std::vector< std::vector< real > > &flux_tensor)
void	navier_stokes_internal_flux (const constants_5moment_t *pC, const solverVariables_t *pSV, const real mu, const real k, const real *q, const real u[3], const real *grad_u[3], const real div_u, const real grad_T[3], std::vector< std::vector< real > > &internal_flux, const real rho_min=std::numeric_limits< real >::epsilon())
real	navier_stokes_numerical_flux (constants_5moment_t *pC, const solverVariables_t *pSV, const real viscosity, const real thermal_conductivity, const real *q_l, const real *q_r, const real *aux_l, const real *aux_r, real *numerical_flux, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	interspeciesCollisions (const real nu_ab, const constants_5moment_t *pC_a, const constants_5moment_t *pC_b, const real *q_a, const real *q_b, real *source, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	calcGradT (const constants_5moment_t *pC, const real *q, const real *aux, const real *grad_u, real *grad_T, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Computes temperature gradients from 5 moment conserved variable gradients/values.
real	calcDivU (const real *q, const real *aux, const real rho_min=std::numeric_limits< real >::epsilon())
void	calcGradU (const real *q, const real *aux, real *grad_u[3], const real rho_min=std::numeric_limits< real >::epsilon())
void	get_mu_and_k (const constants_5moment_t *pC, const real *q, const bool is_neutral, const real collision_coefficient, const real minimum_frequency, const real diffusivity_min, const real diffusivity_max, const bool is_const_mu, const real const_mu, const bool is_const_k, const real const_k, real &mu, real &k, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
real	positivity_preserving_source_dt (const real *q, const real *dqdt, real lambda, const real rho_min=std::numeric_limits< real >::epsilon())
	Computes the maximum allowable dt for a source term to preserve positivity for the positivity-preserving DG scheme.

Function Documentation

antirotateVector()

void wxm::apps::five_moment::antirotateVector	(	const real	Rv[5],
		const solverVariables_t *	pSV,
		real	v[5]
	)

Rotates a 5-moment variable set from local frame to world frame.

Parameters

Rv	Variables in local frame
pSV	Solver variables which define the rotation
v	Resultant variables in world frame

calcDivU()

real wxm::apps::five_moment::calcDivU	(	const real *	q,
		const real *	aux,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

calcGradT()

void wxm::apps::five_moment::calcGradT	(	const constants_5moment_t *	pC,
		const real *	q,
		const real *	aux,
		const real *	grad_u,
		real *	grad_T,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Computes temperature gradients from 5 moment conserved variable gradients/values.

Parameters

q	conserved variables
aux	gradients of conserved variables
grad_u	velocity gradients (pre-computed using grad_u)
grad_T	output temperature gradients
mass	species normalized mass
gamma	species gas gamma

calcGradU()

void wxm::apps::five_moment::calcGradU	(	const real *	q,
		const real *	aux,
		real *	grad_u[3],
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

CtoNC()

void wxm::apps::five_moment::CtoNC	(	const constants_5moment_t *	pC,
		const real	QC[5],
		real	QNC[5],
		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	Normalized minimum mass density
press_min	Normalized minimum pressure.

eulerFlux()

void wxm::apps::five_moment::eulerFlux	(	const constants_5moment_t *	pC,
		const real	QC[5],
		real	flux[5],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Flux along x-axis for Euler fluid equations using conserved variables.

Parameters

pC	Constants that define this specific gas
QC	Conserved variables
flux	Resultant flux
rho_min	Normalized minimum mass density.
press_min	Normalized minimum mass density.

eulerHLLECFluxSolver()

void wxm::apps::five_moment::eulerHLLECFluxSolver	(	const constants_5moment_t *	pC,
		const real	QC_l[5],
		const real	QC_r[5],
		real *	s,
		real	amdq[5],
		real	apdq[5],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

eulerHLLEFluxSolver()

void wxm::apps::five_moment::eulerHLLEFluxSolver	(	const constants_5moment_t *	pC,
		const real	QC_l[5],
		const real	QC_r[5],
		real *	s,
		real	amdq[5],
		real	apdq[5],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Calculates the HLLE flux for the Euler fluid equations.

Parameters

pC	Constants that define this specific gas
pSV	Solver variables
QC_l	Conserved variables of left state
QC_r	Conserved variables of right state
numericalFlux	Resultant numerical flux out of the face

Returns

Suggested dt for this time step

eulerInternalFlux()

real wxm::apps::five_moment::eulerInternalFlux	(	const constants_5moment_t *	pC,
		const solverVariables_t *	pSV,
		const real	QC[5],
		std::vector< std::vector< real > > &	internalFlux,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Calculates the internal euler flux at a given point.

Parameters

pC	Constants that define this specific gas
pSV	Solver variables
QC	Conserved variables
internalFlux	Resultant internal flux

Returns

Suggested dt for this time step

eulerNumericalFlux()

real wxm::apps::five_moment::eulerNumericalFlux	(	const constants_5moment_t *	pC,
		const solverVariables_t *	pSV,
		const real	QC_l[5],
		const real	QC_r[5],
		void(*)(const constants_5moment_t *pC, const real QC_l[5], const real QC_r[5], real *s, real amdq[5], real apdq[5], const real rho_min, const real press_min)	numerical_flux_scheme,
		real	numericalFlux[5],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Calculates the Numerical Flux for the Euler fluid equations using Roe's Method as given by Leveque in "Finite Volume Methods for Hyperbolic Problems" equation 15.40 for a given numerical Flux scheme (Roe, HLLE, etc.)

Parameters

pC	Constants that define this specific gas
pSV	Solver variables
QC_l	Conserved variables of left state
QC_r	Conserved variables of right state
numerical_flux_scheme	Numerical Flux Scheme
numericalFlux	Resultant numerical flux out of the face

Returns

Suggested dt for this time step

eulerNumericalFlux_x()

real wxm::apps::five_moment::eulerNumericalFlux_x	(	const constants_5moment_t *	pC,
		const real	QC_l[5],
		const real	QC_r[5],
		void(*)(const constants_5moment_t *pC, const real QC_l[5], const real QC_r[5], real *s, real amdq[5], real apdq[5], const real rho_min, const real press_min)	numerical_flux_scheme,
		real	flux[5],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Calculates the Euler Numerical flux given a scheme along the x-axis which is to be used as a numerical flux.

Parameters

pC	Constants that define this specific gas
QC_l	Conserved variables for left state
QC_r	Conserved variables for right state
flux	Resultant numerical flux traveling to the right
numerical_flux_scheme	Numerical Flux Scheme

Returns

Fastest absolute wave speed

eulerRoeAverages()

void wxm::apps::five_moment::eulerRoeAverages	(	const constants_5moment_t *	pC,
		const real	ql[5],
		const real	qr[5],
		const real &	pl,
		const real &	pr,
		real &	rho,
		real &	u,
		real &	v,
		real &	w,
		real &	enth,
		real &	a,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

eulerRoeFluxSolver()

void wxm::apps::five_moment::eulerRoeFluxSolver	(	const constants_5moment_t *	pC,
		const real	QC_l[5],
		const real	QC_r[5],
		real *	s,
		real	amdq[5],
		real	apdq[5],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Solves the full Roe decomposition for the euler fluid problem using conserved variables - assumes an entropy fix - function is stolen from WARPX.

Parameters

pC	Constants that define this specific gas
QC_l	Conserved variables describing left state
QC_r	Conserved variables describing right state
s	Resultant wave speeds
amdq	Left traveling fluctuations
apdq	Right traveling fluctuation

eulerRusanovFlux()

real wxm::apps::five_moment::eulerRusanovFlux	(	const constants_5moment_t *	pC,
		const solverVariables_t *	pSV,
		const real	QC_l[5],
		const real	QC_r[5],
		real	numericalFlux[5],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Calculates the Rusanov flux for the Euler fluid equations directly.

Parameters

pC	Constants that define this specific gas
pSV	Solver variables
QC_l	Conserved variables of left state
QC_r	Conserved variables of right state
numericalFlux	Resultant numerical flux out of the face

Returns

Suggested dt for this time step

get_mu_and_k()

void wxm::apps::five_moment::get_mu_and_k	(	const constants_5moment_t *	pC,
		const real *	q,
		const bool	is_neutral,
		const real	collision_coefficient,
		const real	minimum_frequency,
		const real	diffusivity_min,
		const real	diffusivity_max,
		const bool	is_const_mu,
		const real	const_mu,
		const bool	is_const_k,
		const real	const_k,
		real &	mu,
		real &	k,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

getPressureFloored()

real wxm::apps::five_moment::getPressureFloored	(	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 pressure from Euler (5-moment) variables using floors for pressure and density.

The floored pressure is given as

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

where

\[ p = (\gamma - 1) \left( e - \frac{1}{2} \max(\rho, \rho_{min}) v^2) \]

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

Parameters

q	The raw 5-moment 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.

getRhoFloored()

real wxm::apps::five_moment::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 5-moment variables.
rho_min	Normalized minimum mass density.

Returns

Floored mass density.

getTemperatureFloored()

real wxm::apps::five_moment::getTemperatureFloored	(	const real *	q,
		const real	gas_gamma,
		const real	A = 1.0,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Get the temperature from Euler (5-moment) variables using floors for pressure and density.

Temperature is calculated assuming ideal gas law: \( p = n T \)

Therefore

\[ T = \frac{p_{fl}}{\rho_{fl}} A \]

where

\[ p_{fl} = \max(p, p_{min}), \quad \text{and} \quad \rho_{fl} = \max(\rho, \rho_{min}). \]

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

Parameters

q	The raw 5-moment variables.
gas_gamma	Ratio of specific heats.
A	Proton normalized ion mass.
rho_min	Normalized minimum mass density.
press_min	Normalized minimum mass density.

Returns

Temperature calculated assuming pressure and density floors.

hartenHymanEntropyFix()

void wxm::apps::five_moment::hartenHymanEntropyFix	(	const constants_5moment_t *	pC,
		const real	ql[5],
		const real	qr[5],
		const real	s[3],
		const real	wave[][3],
		real	amdq[5],
		real	apdq[5],
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

interspeciesCollisions()

real wxm::apps::five_moment::interspeciesCollisions	(	const real	nu_ab,
		const constants_5moment_t *	pC_a,
		const constants_5moment_t *	pC_b,
		const real *	q_a,
		const real *	q_b,
		real *	source,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

navier_stokes_anisotropic_pressure_tensor()

void wxm::apps::five_moment::navier_stokes_anisotropic_pressure_tensor	(	const real	viscosity,
		const real *	q,
		const real *	grad_rho,
		const real *	grad_p[3],
		real	pi[3][3]
	)

navier_stokes_internal_flux()

void wxm::apps::five_moment::navier_stokes_internal_flux	(	const constants_5moment_t *	pC,
		const solverVariables_t *	pSV,
		const real	mu,
		const real	k,
		const real *	q,
		const real	u[3],
		const real *	grad_u[3],
		const real	div_u,
		const real	grad_T[3],
		std::vector< std::vector< real > > &	internal_flux,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

navier_stokes_numerical_flux()

real wxm::apps::five_moment::navier_stokes_numerical_flux	(	constants_5moment_t *	pC,
		const solverVariables_t *	pSV,
		const real	viscosity,
		const real	thermal_conductivity,
		const real *	q_l,
		const real *	q_r,
		const real *	aux_l,
		const real *	aux_r,
		real *	numerical_flux,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

navier_stokes_viscous_flux_tensor()

void wxm::apps::five_moment::navier_stokes_viscous_flux_tensor	(	const real *	q,
		const solverVariables_t *	pSV,
		const real	pi[][3],
		const real	h[3],
		std::vector< std::vector< real > > &	flux_tensor
	)

NCtoC()

void wxm::apps::five_moment::NCtoC	(	const constants_5moment_t *	pC,
		const real	QNC[5],
		real	QC[5]
	)

Converts nonconserved (primitive) variables to conserved variables.

Parameters

QNC	Nonconserved variables
QC	Resultant conserved variables

NCtoCDifferential()

void wxm::apps::five_moment::NCtoCDifferential	(	const constants_5moment_t *	pC,
		const real	QNC_center[5],
		const real	dQNC[5],
		const real	QC_center[5],
		real	dQC[5]
	)

This currently isn't used anywhere.

Can it be deleted?

positivity_preserving_source_dt()

real wxm::apps::five_moment::positivity_preserving_source_dt	(	const real *	q,
		const real *	dqdt,
		real	lambda,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

Computes the maximum allowable dt for a source term to preserve positivity for the positivity-preserving DG scheme.

Parameters

q	the conserved variables: density, momentum and total (thermal + kinetic) energy, in an array of length 5.
dqdt	the time derivatives of q
lambda	the proportion of the positive densities which should remain after the timestep.

The timestep is computed to be the maximum which satisfies several constraints:

• That \(\rho^n + 2 * \Delta t \dot{\rho^n} > 0\). The factor of 2 is required for the positivity-preserving DG method.
• That \(\rho^n + \Delta t \dot{\rho^n} > \lambda \rho^n\).
• That \(p(\mathbf{q}^n + 2\Delta t \mathbf{q}^n) > 0\).
• That \(p(\mathbf{q}^n + 2\Delta t \mathbf{q}^n) > (1 - 2(1 - \lambda)) p(\mathbf{q}^n)\).

For details on these constraints and how we find a dt that satisfies them, see the writeup.

For MHD< variables, one should subtract off the magnetic energy \(|B|^2/2\) from the fifth element of the variable, q[4], before passing it in to this function.

See also

Writeup document, "Timestep limit for source terms".

rotateVector()

void wxm::apps::five_moment::rotateVector	(	const real	v[5],
		const solverVariables_t *	pSV,
		real	Rv[5]
	)

Rotates a 5-moment variable set from world frame to local frame.

Parameters

v	Variables in world frame
pSV	Solver variables which define the rotation
Rv	Resultant variables in local frame