#include <SSP3.h>

Inheritance diagram for SSP3:

Collaboration diagram for SSP3:

[legend]

Public Member Functions
	SSP3 (Data data, Model model, Bcs bcs, FluxMethod fluxMethod)

virtual	~SSP3 ()

void	step (double cons, double prims, double *aux, double dt=0)

Public Member Functions inherited from SSP2
	SSP2 (Data data, Model model, Bcs bcs, FluxMethod fluxMethod)

virtual	~SSP2 ()

Public Member Functions inherited from TimeIntegrator
	TimeIntegrator (Data data, Model model, Bcs bcs, FluxMethod fluxMethod, ModelExtension *modelExtension=NULL)

virtual	~TimeIntegrator ()

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

Public Member Functions inherited from TimeIntegratorBase
	TimeIntegratorBase (Data data, Model model, Bcs bcs, FluxMethod fluxMethod, ModelExtension *modelExtension=NULL)

virtual	~TimeIntegratorBase ()

Public Attributes
IMEX3Arguments	args


double *	U3

double *	U3guess

double *	source3

double *	flux3

double *	tempprims

double *	tempaux

Public Attributes inherited from SSP2
IMEX2Arguments	args

double *	x

double *	fvec

double *	wa

double *	U1

double *	U2

double *	source1

double *	flux1

double *	source2

double *	flux2

Public Attributes inherited from TimeIntegratorBase
Data *	data

Model *	model

Bcs *	bcs

FluxMethod *	fluxMethod

ModelExtension *	modelExtension

Detailed Description

Implicit-Explicit Runge-Kutta third order SSP3(332) time integrator

: Integrator is third order, solves the non-stiff fluxes explicitly and the (possibly) stiff sources implicitly. Values for the constants and general methods are from Pareschi & Russo 2004.

What follows is a brief description of the method. For a system of conservation equations, given in general by

\begin{align} \partial_t U = F(U) + \psi(U) \end{align}

the third order SSP3(332) IMEX scheme takes the following form:

\begin{align} U^{(1)} &= U^n + \gamma dt \psi(U^{(1)}) \\ U^{(2)} &= U^n + dt \big[F(U^{(1)}) + (1-2\gamma)\psi(U^{(1)}) + \gamma \psi(U^{(2)})\big] \\ U^{(3)} &= U^n + \frac{dt}{4} \big[F(U^{(1)}) + F(U^{(2)})\big] + dt \big[(0.5 - \gamma) \psi(U^{(1)}) + \gamma \psi(U^{(3)})\big] \\ U^{n+1} &= U^n + \frac{dt}{6} \big[F(U^{(1)}) + F(U^{(2)}) + 4F(U^{(3)}) + \psi{U^{(1)}} + \psi(U^{(2)}) + 4\psi(U^{(3)}) \big] \end{align}

.

: The sources are necessarily solved via an implicit rootfind, using a multidimensional Newton-Secant method found here.

Definition at line 34 of file SSP3.h.

Constructor & Destructor Documentation

◆ SSP3()

SSP3::SSP3	(	Data *	data,
		Model *	model,
		Bcs *	bcs,
		FluxMethod *	fluxMethod
	)

Constructor.

: Constructor requires simulation data and the flux and source functions from the model class.

Parameters

*data	Pointer to Data class containing global simulation data
*model	pointer to Model object
*bcs	pointer to Bcs object
*fluxMethod	pointer to FluxMethod object

See also: TimeIntegrator::TimeIntegrator; SSP2::SSP2

◆ ~SSP3()

virtual SSP3::~SSP3 ( )

virtual

Destructor.

Member Function Documentation

◆ step()

void SSP3::step	(	double *	cons,
		double *	prims,
		double *	aux,
		double	dt = `0`
	)

virtual

Performs a single time step.

: The timestep will use the current values of the conserved, primitive and auxiliary variables at t=t0 and compute the values of all of them at time t=t0 + dt. I.e. the conserved vector is evolved forward, and the corresponding prims and aux vars are found.

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
dt	the step size desired to move by. Defaults to the value in the Data class

See also: TimeIntegrator::step; SSP2::step

Reimplemented from SSP2.

Member Data Documentation

◆ args

IMEX3Arguments SSP3::args

IMEX3Arguments, additional arguments class, stores single cell data for hydrb rootfinder.

Definition at line 38 of file SSP3.h.