Multi-block simulations in general relativity: high order discretizations, numerical stability, and applications
arXiv:gr-qc/0507004 · doi:10.1088/0264-9381/22/24/006
Abstract
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the different grids involved. In this work we discuss a technique that allows one to construct finite difference schemes of arbitrary high order which are guaranteed to satisfy linear numerical and strict stability. The technique relies on the use of difference operators satisfying summation by parts and {\it penalty techniques} to transfer information between the grids. This allows the derivation of semidiscrete energy estimates for problems admitting such estimates at the continuum. We analyze several aspects of this technique when used in conjuction with high order schemes and illustrate its use in one, two and three dimensional numerical relativity model problems with non-trivial topologies, including truly spherical black hole excision.
35 pages
References in corpus (11)
- Toward standard testbeds for numerical relativity
- Well posed constraint-preserving boundary conditions for the linearized Einstein equations
- Summation by parts and dissipation for domains with excised regions
- Black Hole Excision with Multiple Grid Patches
- 3D simulations of linearized scalar fields in Kerr spacetime
- Radiative falloff in the background of rotating black hole
- Spherical excision for moving black holes and summation by parts for axisymmetric systems
- 3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints
- The discrete energy method in numerical relativity: Towards long-term stability
- Radiation tails and boundary conditions for black hole evolutions
- Stability properties of a formulation of Einstein's equations
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