#include <srmhd.h>

Inheritance diagram for SRMHD:

Collaboration diagram for SRMHD:

Public Member Functions
	SRMHD ()

	SRMHD (Data *data)

virtual	~SRMHD ()

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 ()

Public Attributes
int	smartGuesses

double *	solution

Public Attributes inherited from Model
Data *	data

int	Ncons

int	Nprims

int	Naux

Detailed Description

Special Relativistic MagnetHydroDynamics

: The single fluid, special relativistic, ideal limit of the MHD equations. Ideal fluid, so resistivity does not play a part, hence no electric field evolution.

Note: Model has nine conserved variables:
\(\ \ \ D\), \(S_x\), \(S_y\), \(S_z\), \(\tau\), \(B_x\), \(B_y\), \(B_z\), \(\phi\)
Eight primitive variables:
\(\ \ \ \rho\), \(v_x\), \(v_y\), \(v_z\), \(p\), \(B_x\), \(B_y\), \(B_z\)
Thirteen auxiliary variables:
\(\ \ \ h\), \(W\), \(e\), \(c\), \(b_0\), \(b_x\), \(b_y\), \(b_z\), \(b^2\), \(v^2\), \(B \cdot S\), \(B^2\), \(S^2\)

: The SRMHD fluid equations are derived from the consideration of the conservation of the rest-mass and stress-energy tensor, and the conservation of the Maxwell dual tensor for a perfect magneto-fluid. That is, starting from
\begin{align} \partial_\mu N^\mu &= 0 \\ \partial_mu T^{\mu \nu}&= 0 \\ \partial_mu {^*}F^{\mu \nu} &= 0 \end{align}
with \(N^\mu = \rho u^mu\) the rest-mass density, \(T^{\mu \nu} = \rho h^* u^\mu u^\nu + \eta^{\mu \nu} p^* - b^mu b^nu\) as the stress-energy tensor for a perfect magneto-fluid, and the Maxwell tensor given by \( {^*}F^{\mu \nu} = u^\mu b^\nu - u^\nu b^\mu\).

: In addition, \( u^\mu, h^*=1+e+p/\rho+b^2/\rho, \rho, \eta, b^\mu \text{ and } p*=p+b^2/2\) are the fluid four-velocity, specific enthalpy including the magnetic contribution, mass-energy density, mostly positive flat space-time metric, four-vector magnetic field in the fluid rest-frame and the total pressure including the magnetic pressure.

: Following this through, we arrive at the conservative form of the special relativistic, ideal limit, single fluid equations of motion:
\begin{align} \partial_t \begin{pmatrix} D \\ S^j \\ \tau \\ B^k \\ \phi \end{pmatrix} + \partial_i \begin{pmatrix} Dv^i \\ S^j v^i + p^* \delta^{ij} - b^j B^i / W \\ \tau v^i + p^* v^i - b^0 B^i/ W \\ v^i B^k - v^k B^i + \delta^{ij}\phi \\ B^i \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ -\phi / c_p^2 \end{pmatrix}. \end{align}

: Here, we sum over the \(i\) coordinate directions, and note the following relations:
\begin{align} D &= \rho W \\ S^j &= \rho h^* W^2 v^j - b^0 b^j \\ \tau &= \rho h^* W^2 - p^* - (b^0)^2 - D \\ u^\mu &= W(c, v^i) \\ W &= 1 / \sqrt(1 - v_i v^i) \\ b^0 &= W B_i v^i \\ b^i &= B^i / W + b^0 v^i \\ b^2 &= B_i B^i / W^2 + (B_i v^i)^2 \\ c_p &= const. \end{align}

: We have also included the additional scalar field \(\phi\) such that any errors in the evolution of the magnetic fields that break the divergence constraint set by Maxwell's equations, namely \(\nabla \cdot B = 0\), are driven to zero, on a timescale set by the constant parameter \(c_p\). See Dedner et al. 2002.

See also: Model

Definition at line 93 of file srmhd.h.

Constructor & Destructor Documentation

◆ SRMHD() [1/2]

SRMHD::SRMHD ( )

Default constructor.

◆ SRMHD() [2/2]

SRMHD::SRMHD ( 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

◆ ~SRMHD()

virtual SRMHD::~SRMHD ( )

virtual

Destructor.

Member Function Documentation

◆ finalise()

void SRMHD::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 230 of file srmhd.h.

◆ fluxVector()

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

virtual

Flux vector.

: Method determines the value for the flux vector.

: For the form of the fluxes see Anton 2010 with the inclusion of divergence cleaning from Dedner et al. 2002. interfaces, John Muddle.

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 \(N_{cons}N_xN_y*N_z\)
*prims	pointer to primitive vector work array. Size is \(N_{prims}N_xN_y*N_z\)
*aux	pointer to auxiliary vector work array. Size is \(N_{aux}N_xN_y*N_z\)
*f	pointer to flux vector work array. Size is \(N_{cons}N_xN_y*N_z\)
dir	direction in which to generate flux vector. \((x, y, z) = (0, 1, 2)\)

See also: Model::fluxVector

Implements Model.

◆ getPrimitiveVars()

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

virtual

Spectral decomposition.

: Method outlined in Anton 2010, Relativistic Magnetohydrodynamcis: Renormalized Eignevectors and Full Wave Decompostiion Riemann Solver. Requires an N=2 rootfind using cminpack library.

: Initial inputs will be the current values of the conserved vector and the old values for the prims and aux vectors. Output will be the current values of cons, prims and aux.

Parameters

*cons	pointer to conserved vector work array. Size is \(N_{cons}N_xN_y*N_z\)
*prims	pointer to primitive vector work array. Size is \(N_{prims}N_xN_y*N_z\)
*aux	pointer to auxiliary vector work array. Size is \(N_{aux}N_xN_y*N_z\)

See also: Model::getPrimitiveVars

Implements Model.

◆ getPrimitiveVarsSingleCell()

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

virtual

Single cell cons2prims conversion.

: For the same reason as outlined in sourceTermSingleCell, some models will require a single celled primitive conversion method.

: Each of the arguments are only for a single cell, ie, cons points to an (Ncons,) array, etc.

Parameters

*cons	pointer to conserved vector work array. Size is \(N_{cons}\)
*prims	pointer to primitive vector work array. Size is \(N_{prims}\)
*aux	pointer to auxiliary vector work array. Size is \(N_{aux}\)
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 SRMHD::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 Anton 2010. Riemann Solver`

Parameters

*cons	pointer to conserved vector work array. Size is \(N_{cons}N_xN_y*N_z\)
*prims	pointer to primitive vector work array. Size is \(N_{prims}N_xN_y*N_z\)
*aux	pointer to auxiliary vector work array. Size is \(N_{aux}N_xN_y*N_z\)

See also: Model::primsToAll

Implements Model.

◆ sourceTerm()

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

virtual

Source term contribution.

: Non-zero flux for cons[8], phi, as a result of implementing divergence cleaning. For details see Muddle.

Parameters

*cons	pointer to conserved vector work array. Size is \(N_{cons}N_xN_y*N_z\)
*prims	pointer to primitive vector work array. Size is \(N_{prims}N_xN_y*N_z\)
*aux	pointer to auxiliary vector work array. Size is \(N_{aux}N_xN_y*N_z\)
*source	pointer to source vector work array. Size is \(N_{cons}N_xN_y*N_z\)

See also: Model::sourceTerm

Implements Model.

◆ sourceTermSingleCell()

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

virtual

Single cell source term contribution.

: Models that can posess a stiff source term and hence (semi-)implicit time integrators will require a source contribution (and cons2prims method) that applies to a single cell.

: Each of the arguments are only for a single cell, ie, cons points to an (Ncons,) array, etc.

Parameters

*cons	pointer to conserved vector work array. Size is \(N_{cons}\)
*prims	pointer to primitive vector work array. Size is \(N_{prims}\)
*aux	pointer to auxiliary vector work array. Size is \(N_{aux}\)
*source	pointer to source vector work array. Size is \(N_{cons}\)
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.

Member Data Documentation

◆ smartGuesses

int SRMHD::smartGuesses

Number of smart guess required.

Definition at line 98 of file srmhd.h.

◆ solution

double* SRMHD::solution

Pointer to array to hold solution of C2P for every cell. Size is 2*Nx*Ny*Nz.

Definition at line 100 of file srmhd.h.

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

srmhd.h

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SRMHD() [1/2]

◆ SRMHD() [2/2]

◆ ~SRMHD()

Member Function Documentation

◆ finalise()

◆ fluxVector()

◆ getPrimitiveVars()

◆ getPrimitiveVarsSingleCell()

◆ primsToAll()

◆ sourceTerm()

◆ sourceTermSingleCell()

Member Data Documentation

◆ smartGuesses

◆ solution