#include <REGIME.h>

Inheritance diagram for REGIME:

Collaboration diagram for REGIME:

[legend]

Public Member Functions
	REGIME ()

	REGIME (Data data, FluxMethod fluxMethod)

virtual	~REGIME ()

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

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

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

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

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

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

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

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

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

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

Public Member Functions inherited from ModelExtension
	ModelExtension ()

	ModelExtension (Data *data)

virtual	~ModelExtension ()

virtual void	fluxExtension (double cons, double prims, double aux, double flux)

Public Attributes
double *	dfxdw

double *	dfydw

double *	dfzdw

double *	dwdsb

double *	E

double *	q

double *	K

double *	Mx

double *	My

double *	Mz

double *	fbx

double *	fby

double *	fbz

double *	diffuX

double *	diffuY

double *	diffuZ

double *	alpha

FluxMethod *	fluxMethod

Public Attributes inherited from ModelExtension
Data *	data

bool	sourceExists

bool	fluxExists

Detailed Description

REGIME: Resistive extension upgrade for ideal MHD

This class represents the implementation of REGIME, a resistive extension to the special relativistic, ideal MHD equations. Details can be found in Wright & Hawke 2019 A resistive extension to ideal MHD.

REGIME extends the equations of ideal MHD by means of an additional, diffusive source term. The new system has the following form:

\begin{align} \frac{\partial q}{\partial t} + \frac{\partial f^i(q)}{\partial x^i} = \frac{\partial D^i}{\partial x^i} \end{align}

where the LHS corresponds to the standard, special relativistic ideal MHD (SRMHD) equations, and the RHD is the source term extension of REGIME.

The diffusion vector is defined by the following:

\begin{align} D^i = -\frac{\partial f^i}{\partial \overline{q}} \bigg( \frac{\partial \overline{s}_0}{\partial \overline{q}} \bigg)^{-1} \frac{\partial \overline{f}^j_0}{\partial x^j} \end{align}

where \( f^i \) is the \(i^{th}\) direction, ideal MHD flux, \( \overline{q} \) is the stiff variables (electric fields of resistive MHD), \( \overline{s} \) is the source of the stiff variables and \(\overline{f}^j\) is the \(j^{th}\) flux of the stiff variables.

Within this code, we use the following naming conventions:

dfxdw, dfydw and dfzdw are the derivatives of the \(x\), \(y\) and \(z\) direction fluxes with respect to the primitive variables.
dwdsb is the inverse of the stiff source vector with respect to the primitive variables.
Mx, My, and Mz are the matrices \( -\frac{\partial f^i}{\partial w} \bigg( \frac{\partial \overline{s}_0}{\partial w} \bigg)^{-1} \).
diffuX, diffuY, and diffuZ are the \(D^i\) vectors.

To understand the elements of this extension, please view the paper. Including this extension is as simple as declaring REGIME modelExtension(&data, &fluxMethod); in main, and including a pointer to modelExtension in the time integrator's constructor. With this, the SRMHD model will be able to capture resistive effects. You should play with the model to get a feel for how it behaves with \( \sigma \), and make sure that for high resolution simulations you check that the resolution criterion is met (available in the paper). You may need to reduce the CFL factor if simulations look unstable. Although simulations may converge with conductivities as low as \( \sigma = 10 \), I would be very careful for values less than 50. Conductivities of 100 or more are reliably converging, but remember for smaller conductivities, higher order moments may become important and solutions may differ from resistive MHD.

Optimisations

To improve the performance of REGIME, we have implemented a number of optimisations. These will make the source faster to compute, but may have led to a slightly less readable code (and less modular than I would have liked). We list some of these below:

First note that the vector elements D1, D2, and D3 inside dwdsb (Note: not the diffusion vector!) are not calculated. This is because in all cases the elements are multiplied by zero.
When dotting dfdw with dwdsb, many of the elements are zero and so we manually multiply many of the non-zero entries to save on computation.
A number of loops have been fused together to improve the memory management.

Examples

The best way to understand this extension is to view the examples we have provided. Run the main programs with make run and observe the results using the interactivePlot script.

Definition at line 81 of file REGIME.h.

Constructor & Destructor Documentation

◆ REGIME() [1/2]

REGIME::REGIME ( )

◆ REGIME() [2/2]

REGIME::REGIME	(	Data *	data,
		FluxMethod *	fluxMethod
	)

Constructor.

◆ ~REGIME()

virtual REGIME::~REGIME ( )

virtual

Destructor.

Member Function Documentation

◆ set_dfxdw()

void REGIME::set_dfxdw	(	double *	cons,
		double *	prims,
		double *	aux
	)

Sets the derivative of the non-stiff flux wrt the primitive vector.

◆ set_dfydw()

void REGIME::set_dfydw	(	double *	cons,
		double *	prims,
		double *	aux
	)

◆ set_dfzdw()

void REGIME::set_dfzdw	(	double *	cons,
		double *	prims,
		double *	aux
	)

◆ set_dwdsb()

void REGIME::set_dwdsb	(	double *	cons,
		double *	prims,
		double *	aux
	)

Sets the derivative of the primitive vector wrt the stiff source vector.

◆ set_Dx()

void REGIME::set_Dx	(	double *	cons,
		double *	prims,
		double *	aux
	)

Set the diffusion vector. Method assumes K and dwdsb are set.

◆ set_Dy()

void REGIME::set_Dy	(	double *	cons,
		double *	prims,
		double *	aux
	)

◆ set_Dz()

void REGIME::set_Dz	(	double *	cons,
		double *	prims,
		double *	aux
	)

◆ set_K()

void REGIME::set_K	(	double *	cons,
		double *	prims,
		double *	aux
	)

Determines the RHS bracket of the diffusion terms.

I.e.

\begin{align} K &= \partial_a \overline{f}^a - \partial_w \overline{q}_0 (\partial_w q)^{-1} \partial_a f^a \\ &= \partial_a \overline{f}^a \end{align}

for the resistive model. Recall M2 = 0.

◆ set_vars()

void REGIME::set_vars	(	double *	cons,
		double *	prims,
		double *	aux
	)

Sets up variables including the electric field and charge density.

◆ sourceExtension()

void REGIME::sourceExtension	(	double *	cons,
		double *	prims,
		double *	aux,
		double *	source
	)

virtual

Main user function for the modified source.

This method implements the modified source for REGIME. Given the current state of the system in cons, prims and aux, it writes into source the contribution from the derivative of the diffusion vector.

Parameters

[in]	*cons	pointer to conserved vector work array. Size is \(N_{cons} \times N_x \times N_y \times N_z\)
[in]	*prims	pointer to primitive vector work array. Size is \(N_{prims} \times N_x \times N_y \times N_z\)
[in]	*aux	pointer to auxiliary vector work array. Size is \(N_{aux} \times N_x \times N_y \times N_z\)
[out]	*source	pointer to source vector work array. Size is \(N_{cons} \times N_x \times N_y \times N_z\)

See also: ModelExtension

Reimplemented from ModelExtension.

Member Data Documentation

◆ alpha

double * REGIME::alpha

Prefactor for dwdsb.

Definition at line 87 of file REGIME.h.

◆ dfxdw

double* REGIME::dfxdw

Definition at line 87 of file REGIME.h.

◆ dfydw

double * REGIME::dfydw

Definition at line 87 of file REGIME.h.

◆ dfzdw

double * REGIME::dfzdw

Derivative of flux vector wrt to primitive variables.

Definition at line 87 of file REGIME.h.

◆ diffuX

double * REGIME::diffuX

Definition at line 87 of file REGIME.h.

◆ diffuY

double * REGIME::diffuY

Definition at line 87 of file REGIME.h.

◆ diffuZ

double * REGIME::diffuZ

Diffusion vector.

Definition at line 87 of file REGIME.h.

◆ dwdsb

double * REGIME::dwdsb

Derivative of primitive vector wrt stiff source.

Definition at line 87 of file REGIME.h.

◆ E

double * REGIME::E

Electric field vector.

Definition at line 87 of file REGIME.h.

◆ fbx

double * REGIME::fbx

Definition at line 87 of file REGIME.h.

◆ fby

double * REGIME::fby

Definition at line 87 of file REGIME.h.

◆ fbz

double * REGIME::fbz

Stiff flux vector.

Definition at line 87 of file REGIME.h.

◆ fluxMethod

FluxMethod* REGIME::fluxMethod

Pointer to the flux method class.

Definition at line 104 of file REGIME.h.

◆ K

double * REGIME::K

partial_a fbar^a

Definition at line 87 of file REGIME.h.

◆ Mx

double * REGIME::Mx

Definition at line 87 of file REGIME.h.

◆ My

double * REGIME::My

Definition at line 87 of file REGIME.h.

◆ Mz

double * REGIME::Mz

Directional matrices multiplying K. Dot prod(partial_w f^a, partial_sbar w)

Definition at line 87 of file REGIME.h.

◆ q

double * REGIME::q

Charge density.

Definition at line 87 of file REGIME.h.

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

REGIME.h

Public Member Functions

Public Attributes

Detailed Description

Optimisations

Examples

Constructor & Destructor Documentation

◆ REGIME() [1/2]

◆ REGIME() [2/2]

◆ ~REGIME()

Member Function Documentation

◆ set_dfxdw()

◆ set_dfydw()

◆ set_dfzdw()

◆ set_dwdsb()

◆ set_Dx()

◆ set_Dy()

◆ set_Dz()

◆ set_K()

◆ set_vars()

◆ sourceExtension()

Member Data Documentation

◆ alpha

◆ dfxdw

◆ dfydw

◆ dfzdw

◆ diffuX

◆ diffuY

◆ diffuZ

◆ dwdsb

◆ E

◆ fbx

◆ fby

◆ fbz

◆ fluxMethod

◆ K

◆ Mx

◆ My

◆ Mz

◆ q