A cartesian grid embedded boundary method for hyperbolic conservation laws
We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L{sup 1} for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Director. Office of Science. Office of Advanced Scientific Computing Research. Mathematical Information and Computing Sciences Division, Computational Science Graduate Fellowship Contract DE-FG02-97ER25308. Sandia National Laboratory (US)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 841320
- Report Number(s):
- LBNL-56420; R&D Project: KS1110; TRN: US200513%%611
- Journal Information:
- Journal of Computational Physics, Vol. 51, Issue 12; Other Information: Submitted to Journal of Computational Physics: Volume 51, No.12; Journal Publication Date: 12/2004; PBD: 3 Oct 2004
- Country of Publication:
- United States
- Language:
- English
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