#include <twoFluidEMHD.h>

Inheritance diagram for TwoFluidEMHD:

Collaboration diagram for TwoFluidEMHD:

Public Member Functions
	TwoFluidEMHD ()

	TwoFluidEMHD (Data *data)

virtual	~TwoFluidEMHD ()

void	sourceTermSingleCell (double cons, double prims, double aux, double source, int i=-1, int j=-1, int k=-1)

void	sourceTerm (double cons, double prims, double aux, double source)

void	getPrimitiveVarsSingleCell (double cons, double prims, double *aux, int i=-1, int j=-1, int k=-1)

void	getPrimitiveVars (double cons, double prims, double *aux)

void	primsToAll (double cons, double prims, double *aux)

void	fluxVector (double cons, double prims, double aux, double f, const int dir)

void	finalise (double cons, double prims, double *aux)

Public Member Functions inherited from Model
	Model ()

	Model (Data *data)

virtual	~Model ()

Additional Inherited Members
Public Attributes inherited from Model
Data *	data

int	Ncons

int	Nprims

int	Naux

Detailed Description

Two-Fluid ElectroMagnetoHydroDynamics

: The special relativistic, two fluid model of EMHD. Governing equations have been taken and adapted from Amano 2016.

: We label the species 1 and 2, so the density of electrons may be rho1 and of positrons may be rho2 for example.

Note: The model has eighteen conserved variables:
\( \ \ \ D, S_x, S_y, S_z, \tau \\ \ \ \ \bar{D}, \bar{S}_x, \bar{S}_y, \bar{S}_z, \bar{\tau}, \\ \ \ \ B_x, B_y, B_z, \\ \ \ \ E_x, E_y, E_z, \\ \ \ \ \psi, \phi \)
Sixteen primitive variables:
\( \ \ \ \rho_1, v_{x1}, v_{y1}, v_{z1}, p_1, \\ \ \ \ \rho_2, v_{x2}, v_{y2}, v_{z2}, p_2, \\ \ \ \ B_x, B_y, B_z, \\ \ \ \ E_x, E_y, E_z \)
Thirty-five auxiliary variables:
\( \ \ \ h_1, W_1, e_1, v^2_1, Z_1, D_1, \tilde{S}_{x1}, \tilde{S}_{y1}, \tilde{S}_{z1}, \tilde{\tau}_1, \\ \ \ \ h_2, W_2, e_2, v^2_2, Z_2, D_2, \tilde{S}_{x2}, \tilde{S}_{y2}, \tilde{S}_{z2}, \tilde{\tau}_2, \\ \ \ \ J_x, J_y, J_z, \\ \ \ \ \tilde{S}_x, \tilde{S}_y, \tilde{S}_z, \tilde{\tau}, \\ \ \ \ B^2, E^2 \\ \ \ \ \mathcal{\varrho}_0, \mathcal{\varrho}, \\ \ \ \ u_x, u_y, u_z, W \)

: The two fluid EMHD equations describe a plasma composed of two oppositely charged species, electrons and positrons. We evolve the species by summing and differencing their standard hydrodynamical properties, and thus consider the following system of conservation equations:
\begin{align} \partial_t \renewcommand\arraystretch{5.0} \begin{pmatrix} D \\ S^x \\ S^y \\ S^z \\ \tau \\ \bar{D} \\ \bar{S}^x \\ \bar{S}^y \\ \bar{S}^z \\ \bar{\tau} \\ B^x \\ B^y \\ B^z \\ E^x \\ E^y \\ E^z \\ \psi \\ \phi \end{pmatrix} + \partial_j \begin{pmatrix} \rho_s W_s v_s^j \\ \rho_s h_s W_s^2 v_{s,x} v_s^j - (E_x E^j + B_x B^j) + \delta_x^j [(E^2 + B^2) / 2+ p_s ] \\ \rho_s h_s W_s^2 v_{s,y} v_s^j - (E_y E^j + B_y B^j) + \delta_y^j [(E^2 + B^2) / 2+ p_s ] \\ \rho_s h_s W_s^2 v_{s,z} v_s^j - (E_z E^j + B_z B^j) + \delta_z^j [(E^2 + B^2) / 2+ p_s ] \\ \rho_s h_s W_s^2 v_s^i + \epsilon^{jkl} E_k B_l - \rho_s W_s v_s^j \\ \mu_s \rho_s W_s v_s^j \\ \mu_s \rho_s h_s W_s^2 v_{s, x} v_s^j + \delta_x^j \mu_s p_s \\ \mu_s \rho_s h_s W_s^2 v_{s, y} v_s^j + \delta_y^j \mu_s p_s \\ \mu_s \rho_s h_s W_s^2 v_{s, z} v_s^j + \delta_z^j \mu_s p_s \\ \mu_s \rho_s h_s W_s^2 v_s^i - \mu_s \rho_s W_s v_s^i \\ \epsilon^{ixj} E_i + \delta_x^j \phi \\ \epsilon^{iyj} E_i + \delta_y^j \phi \\ \epsilon^{izj} E_i + \delta_z^j \phi \\ -\epsilon^{ixj} B_i + \delta_x^j \psi \\ -\epsilon^{iyj} B_i + \delta_y^j \psi \\-\epsilon^{izj} B_i + \delta_z^j \psi \\ E^j \\ B^j \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ \omega_p^2 \big[ W E^x + (u^y B^z - u^z B^y) - (J^x - \varrho_0 u^x) / \sigma) \\ \omega_p^2 \big[ W E^y + (u^z B^x - u^x B^z) - (J^y - \varrho_0 u^y) / \sigma) \\ \omega_p^2 \big[ W E^z + (u^x B^y - u^y B^x) - (J^z - \varrho_0 u^z) / \sigma) \\ \omega_p^2 \big[u_i E^i - (\varrho - \varrho_0 W) / \sigma\big] \\ 0 \\ 0 \\ 0 \\ -J_x \\ -J_y \\ -J_z \\ \varrho - \psi / c_p^2 \\ -\phi / c_p^2 \end{pmatrix}. \end{align}

: For a comprehensive discussion on this model see Amano 2016.

Definition at line 90 of file twoFluidEMHD.h.

Constructor & Destructor Documentation

◆ TwoFluidEMHD() [1/2]

TwoFluidEMHD::TwoFluidEMHD ( )

Default constructor.

◆ TwoFluidEMHD() [2/2]

TwoFluidEMHD::TwoFluidEMHD ( Data * data )

Parameterized constructor.

Stores a pointer to the Data class for reference in its methods

Parameters

*data Pointer to Data class containing global simulation data

◆ ~TwoFluidEMHD()

virtual TwoFluidEMHD::~TwoFluidEMHD ( )

inlinevirtual

Destructor.

Definition at line 105 of file twoFluidEMHD.h.

Member Function Documentation

◆ finalise()

void TwoFluidEMHD::finalise	(	double *	cons,
		double *	prims,
		double *	aux
	)

inlinevirtual

Finalise the simulation variables.

: Mostly, this probably wont be needed, but if there is any final steps to finish off a timestep, this can be done here.

Reimplemented from Model.

Definition at line 214 of file twoFluidEMHD.h.

◆ fluxVector()

void TwoFluidEMHD::fluxVector	(	double *	cons,
		double *	prims,
		double *	aux,
		double *	f,
		const int	dir
	)

virtual

Flux vector.

Method determines the value of the conserved vector in the specified direction. For the form of the fluxes see Anton 2010, with the inclusion of divergence cleaning from Muddle 2016.

Note: We are assuming that all primitive and auxiliary variables are up-to-date at the time of this function execution.

Parameters

*cons	pointer to conserved vector work array. Size is NconsNxNy*Nz
*prims	pointer to primitive vector work array. Size is NprimsNxNy*Nz
*aux	pointer to auxiliary vector work array. Size is NauxNxNy*Nz
*f	pointer to flux vector work array. Size is NconsNxNy*Nz
dir	direction in which to generate flux vector. (x, y, z) = (0, 1, 2)

See also: Model::fluxVector

Implements Model.

◆ getPrimitiveVars()

void TwoFluidEMHD::getPrimitiveVars	(	double *	cons,
		double *	prims,
		double *	aux
	)

virtual

Spectral decomposition.

Generates the values of the primitive and auxiliary variables consistent with the conservative vector given. Method first separates the fluids, then subtracts the EM fields implementing a resistive MHD single fluid proceedure to each species. Function calls single celled version (below) for each compute cell.

Parameters

*cons	pointer to conserved vector work array. Size is NconsNxNy*Nz
*prims	pointer to primitive vector work array. Size is NprimsNxNy*Nz
*aux	pointer to auxiliary vector work array. Size is NauxNxNy*Nz

See also: Model::getPrimitiveVars

Implements Model.

◆ getPrimitiveVarsSingleCell()

void TwoFluidEMHD::getPrimitiveVarsSingleCell	(	double *	cons,
		double *	prims,
		double *	aux,
		int	i = `-1`,
		int	j = `-1`,
		int	k = `-1`
	)

virtual

Single cell spectral decomposition.

Generates the values for aux and prims for the given cons vector for only a single cell (i, j, k). Note : pointers to arrays are the (Ncons,) conservative array, (Nprims,) prim array and (Naux,) aux array, NOT the (Ncons, Nx, Ny, Nz) arrays as in most other functions. Single celled version required for the inside of the residual functions for the (semi) implicit time integrators.

Parameters

*cons	pointer to conserved vector work array. Size is Ncons
*prims	pointer to primitive vector work array. Size is Nprims
*aux	pointer to auxiliary vector work array. Size is Naux
i	cell number in x-direction (optional)
j	cell number in y-direction (optional)
k	cell number in z-direction (optional)

See also: Model::getPrimitiveVarsSingleCell

Implements Model.

◆ primsToAll()

void TwoFluidEMHD::primsToAll	(	double *	cons,
		double *	prims,
		double *	aux
	)

virtual

Primitive-to-all transformation.

Transforms the initial state given in primitive form in to the conserved vector state. Relations have been taken from Amano 2016.

Parameters

*cons	pointer to conserved vector work array. Size is NconsNxNy*Nz
*prims	pointer to primitive vector work array. Size is NprimsNxNy*Nz
*aux	pointer to auxiliary vector work array. Size is NauxNxNy*Nz

See also: Model::primsToAll

Implements Model.

◆ sourceTerm()

void TwoFluidEMHD::sourceTerm	(	double *	cons,
		double *	prims,
		double *	aux,
		double *	source
	)

virtual

Source term contribution.

Source terms arise from the weighted sum of the species conserved vectors and from implementing the divergence cleaning method. This function determines the source contribution to the change in the conserved vector for all cells. This function calls sourceTermSingleCell for every compute cell.

Parameters

*cons	pointer to conserved vector work array. Size is NconsNxNy*Nz
*prims	pointer to primitive vector work array. Size is NprimsNxNy*Nz
*aux	pointer to auxiliary vector work array. Size is NauxNxNy*Nz
*source	pointer to source vector work array. Size is NconsNxNy*Nz

See also: Model::sourceTerm

Implements Model.

◆ sourceTermSingleCell()

void TwoFluidEMHD::sourceTermSingleCell	(	double *	cons,
		double *	prims,
		double *	aux,
		double *	source,
		int	i = `-1`,
		int	j = `-1`,
		int	k = `-1`
	)

virtual

Single cell source term contribution.

Determines the source vector due the the cond prims and aux vector of a single compute cell. Note : pointers to arrays are the (Ncons,) conservative array, (Nprims,) prim array and (Naux,) aux array, NOT the (Ncons, Nx, Ny, Nz) arrays as in most other functions.

Parameters

*cons	pointer to conserved vector work array. Size is Ncons
*prims	pointer to primitive vector work array. Size is Nprims
*aux	pointer to auxiliary vector work array. Size is Naux
*source	pointer to source vector work array. Size is Ncons
i	cell number in x-direction (optional)
j	cell number in y-direction (optional)
k	cell number in z-direction (optional)

See also: Model::sourceTermSingleCell

Implements Model.

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

twoFluidEMHD.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TwoFluidEMHD() [1/2]

◆ TwoFluidEMHD() [2/2]

◆ ~TwoFluidEMHD()

Member Function Documentation

◆ finalise()

◆ fluxVector()

◆ getPrimitiveVars()

◆ getPrimitiveVarsSingleCell()

◆ primsToAll()

◆ sourceTerm()

◆ sourceTermSingleCell()