A cartesian grid embedded boundary method for hyperbolic conservation laws

Journal Article · Sun Oct 03 04:00:00 EDT 2004 · Journal of Computational Physics

OSTI ID:841320

Colella, Phillip ^[1]; Graves, Daniel T; Keen, Benjamin J; Modiano, David

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1. LBNL Library

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: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• 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
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 12 Vol. 51
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CONSERVATION LAWS
STABILITY