exahype2.api.rkfd4 Namespace Reference

Fourth-order Finite Differences with explicit Runge-Kutta time stepping over block-structured meshes. More...

Namespaces
namespace	actionsets
namespace	AdaptMeshAndBalanceLoad
namespace	central
	-differences-with-runge-kutta-illustrations
namespace	central-differences-with-runge-kutta-illustrations
namespace	CentralDifferencesWithRungeKutta
namespace	FD4Kernels
namespace	PlotAsVTKFile
namespace	Quantities
	Selection of entries of Q by name or index.
namespace	SetupSimulationOverRegularGrid
namespace	WriteCheckpoint

Detailed Description

Fourth-order Finite Differences with explicit Runge-Kutta time stepping over block-structured meshes.

The package is the successor of the legacy exahype2.solvers.rkfd.fd4. It lives parallel to exahype2.api.fv and does not depend on it: grid construction, plotting and all action sets are its own. The Runge-Kutta coefficients come from exahype2.api.rungekutta, which does not depend on the discretisation in space.

Each mesh cell hosts a patch of patch_size^d cell-centred grid cells. The fourth-order stencils reach two grid cells into the neighbouring patches, so each patch is surrounded by a halo of two grid cells, which is reconstructed from the faces. The scheme has no artificial dissipation. exagrype.api.FD4WithKODissipation adds a Kreiss-Oliger dissipation on top, with a halo of three grid cells.

The numerical scheme is exahype2.api.rkfd4.CentralDifferencesWithRungeKutta.CentralDifferencesWithRungeKutta. Its DSLHyPE kernels reside in exahype2.api.rkfd4.FD4Kernels.