Fourth-order Finite Differences with Kreiss-Oliger dissipation. More...

Inheritance diagram for exagrype.api.FD4WithKODissipation.FD4WithKODissipation:

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Collaboration diagram for exagrype.api.FD4WithKODissipation.FD4WithKODissipation:

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Public Member Functions
	__init__ (self, exahype2.api.Solver solver, int patch_size, int rk_order, float kreiss_oliger_sigma, List[Union[str, int]] quantities=None, float time_step_size=None, float cfl_constant=0.5, exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.RightHandSideKernel right_hand_side_kernel=exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.RightHandSideKernel.CentralDifferences, advection_velocity=None, advected_quantities=None)

Public Member Functions inherited from exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta
int	overlap (self)
	Width of the halo, i.e.

int	rk_order (self)

bool	has_adaptive_time_step_size (self)

str	right_hand_side_kernel_name (self)
	Name of the generated right-hand side kernel.

str	max_eigenvalue_kernel_name (self)

Solver.MeshAdaptation	create_default_mesh_adaptation (self)
	The finite differences adapt the mesh and balance the load through exahype2.api.rkfd4.AdaptMeshAndBalanceLoad by default.

"toolbox.blockstructured.api.RestrictHangingFaces"	create_restriction_of_hanging_faces (self)
	Action set which restricts the projected fine data from the hanging faces onto the coarse faces.

	construct_output (self, exahype2_project, peano_project, time_step)
	Add the data to the Peano 4 project, generate the kernels and add the tasks of one Runge-Kutta step to time_step.

Static Public Attributes
int	HALO_SIZE = 3

Static Public Attributes inherited from exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta
int	HALO_SIZE = 2
	Width of the halo.

Protected Member Functions
	_right_hand_side_action_sets (self, stage, cell_guard)
	The plain right-hand side of the superclass, followed by the dissipation.

Protected Member Functions inherited from exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta
	_patches (self)
	All patches of this numerical scheme, i.e.

Protected Attributes
	_solver

Protected Attributes inherited from exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta
	_solver
	Project the outcome onto the faces.

Protected Attributes inherited from exahype2.api.Solver.Solver.NumericalScheme
	_solver

Detailed Description

Fourth-order Finite Differences with Kreiss-Oliger dissipation.

The numerical scheme is exahype2.api.rkfd4.CentralDifferencesWithRungeKutta plus a Kreiss-Oliger dissipation of sixth order on top: Per Runge-Kutta stage, it first evaluates the plain fourth-order right-hand side and then adds

\( \\frac{\\sigma}{64 \\Delta x_d} (Q_{i-3} - 6 Q_{i-2} + 15 Q_{i-1} - 20 Q_i + 15 Q_{i+1} - 6 Q_{i+2} + Q_{i+3}) \)

per axis d to the selected quantities (exagrype.api.actionsets.AddKreissOligerDissipation). Both kernels read the same stage input, i.e. the outcome is the right-hand side with dissipation. The dissipation stencil reaches three grid cells into the neighbouring patches, so the scheme widens the halo from two to three grid cells. Everything else is inherited.

To use the dissipation, replace the numerical scheme of a solver:

solver.numerical_scheme  = exagrype.api.FD4WithKODissipation(solver, patch_size=9, rk_order=4, kreiss_oliger_sigma=8.0)
solver.grid_construction = exahype2.api.rkfd4.SetupSimulationOverRegularGrid(solver, volume_size=0.04)
solver.plotter           = exahype2.api.rkfd4.PlotAsVTKFile(solver, time_in_between_plots=0.1)

The grid construction and the plotter remain those of exahype2.api.rkfd4. The legacy ExaGRyPE runs used kreiss_oliger_sigma=8.0. The scheme is three-dimensional only, as it relies on exagrype::ccz4::addKreissOligerDissipation().

Definition at line 13 of file FD4WithKODissipation.py.

Constructor & Destructor Documentation

◆ init()

exagrype.api.FD4WithKODissipation.FD4WithKODissipation.__init__	(		self,
		exahype2.api.Solver	solver,
		int	patch_size,
		int	rk_order,
		float	kreiss_oliger_sigma,
		List[Union[str, int]]	quantities = `None`,
		float	time_step_size = `None`,
		float	cfl_constant = `0.5`,
		exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.RightHandSideKernel	right_hand_side_kernel = `exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.RightHandSideKernel.CentralDifferences`,
			advection_velocity = `None`,
			advected_quantities = `None`
	)

Parameters

solver	exahype2.api.Solver The solver this numerical scheme realises.
patch_size	int Number of grid cells per axis within one patch. Has to be at least HALO_SIZE=3.
rk_order	int Order of the Runge-Kutta scheme, i.e. its number of stages.
kreiss_oliger_sigma	float Scaling of the Kreiss-Oliger dissipation. Has to be non-negative.
quantities	List[str or int] or None The unknowns which are subject to the dissipation. None, the default, selects all unknowns. A string is the name of an unknown as passed to the solver (e.g. "lapse" or "G" for exagrype.api.CCZ4Solver) and selects all of its entries. An int is the index of one entry of the unknowns. Auxiliary variables do not evolve in time and hence cannot be selected.
time_step_size	float or None Fixed time step size. If None, the time step size is adaptive.
cfl_constant	float CFL constant for adaptive time step sizes.
right_hand_side_kernel	exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.RightHandSideKernel The kernel which evaluates the right-hand side before the dissipation is added,

See also: exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.

Parameters

advection_velocity str or List[str or int] or None Only for lopsided advection,

See also: exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.

Parameters

advected_quantities List[str or int] or None Only for lopsided advection,

See also: exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.

Reimplemented from exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta.

Definition at line 49 of file FD4WithKODissipation.py.

References exagrype.api.FD4WithKODissipation.FD4WithKODissipation.__init__().

Referenced by exagrype.api.FD4WithKODissipation.FD4WithKODissipation.__init__().

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Member Function Documentation

◆ _right_hand_side_action_sets()

exagrype.api.FD4WithKODissipation.FD4WithKODissipation._right_hand_side_action_sets	(	self,
		stage,
		cell_guard
	)

protected

The plain right-hand side of the superclass, followed by the dissipation.

Reimplemented from exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta.

Definition at line 127 of file FD4WithKODissipation.py.

References exagrype.api.FD4WithKODissipation.FD4WithKODissipation._right_hand_side_action_sets().

Referenced by exagrype.api.FD4WithKODissipation.FD4WithKODissipation._right_hand_side_action_sets().

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Field Documentation

◆ _solver

exagrype.api.FD4WithKODissipation.FD4WithKODissipation._solver

protected

Definition at line 133 of file FD4WithKODissipation.py.

◆ dissipative_quantities

exagrype.api.FD4WithKODissipation.FD4WithKODissipation.dissipative_quantities

Definition at line 121 of file FD4WithKODissipation.py.

◆ HALO_SIZE

int exagrype.api.FD4WithKODissipation.FD4WithKODissipation.HALO_SIZE = 3

static

Definition at line 47 of file FD4WithKODissipation.py.

Referenced by exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta.__create_data_structures(), and exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta.overlap().

◆ kreiss_oliger_sigma

exagrype.api.FD4WithKODissipation.FD4WithKODissipation.kreiss_oliger_sigma

Definition at line 120 of file FD4WithKODissipation.py.

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

src/exagrype/api/FD4WithKODissipation.py

Data Fields
	kreiss_oliger_sigma

	dissipative_quantities

Data Fields inherited from exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta
	interpolation

	restriction

	right_hand_side_kernel

	advection_velocity

	advected_quantities

	HALO_SIZE

	patch_size

	min_volume_size

	max_volume_size

	butcher_tableau

	time_step_size

	cfl_constant

	kernel_namespace

	max_eigenvalue_kernel_call

	right_hand_side_kernel_name

	max_eigenvalue_kernel_name

	rk_order

Public Member Functions

Data Fields

Static Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ __init__()

Member Function Documentation

◆ _right_hand_side_action_sets()

Field Documentation

◆ _solver

◆ dissipative_quantities

◆ HALO_SIZE

◆ kreiss_oliger_sigma

◆ init()