A cartesian grid embedded boundary method for hyperbolic conservation laws

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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 ... continued below

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30 pages

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Colella, Phillip; Graves, Daniel T.; Keen, Benjamin J. & Modiano, David October 3, 2004.

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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.

Physical Description

30 pages

Notes

OSTI as DE00841320

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  • Journal Name: Journal of Computational Physics; Journal Volume: 51; Journal Issue: 12; Other Information: Submitted to Journal of Computational Physics: Volume 51, No.12; Journal Publication Date: 12/2004

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  • Report No.: LBNL--56420
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 841320
  • Archival Resource Key: ark:/67531/metadc788989

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  • October 3, 2004

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  • Dec. 3, 2015, 9:30 a.m.

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  • April 4, 2016, 2:54 p.m.

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Colella, Phillip; Graves, Daniel T.; Keen, Benjamin J. & Modiano, David. A cartesian grid embedded boundary method for hyperbolic conservation laws, article, October 3, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc788989/: accessed October 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.