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...

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Bibliographic Details
Published in:Journal of computational physics Vol. 211; no. 1; pp. 347 - 366
Main Authors: Colella, Phillip, Graves, Daniel T., Keen, Benjamin J., Modiano, David
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 2006
Elsevier
Subjects:
Boundaries
Cartesian
Computational techniques
Conservation laws
Discontinuity
Discretization
Exact sciences and technology
Hyperbolic systems
Mathematical methods in physics
Physics
Preserves
Stability
Conservation laws
Discontinuity
Second order
Hyperbolic system
Algorithms
Discretization
Mass difference
Calculation
Calculation methods
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary: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 1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2005.05.026