A Cartesian grid embedded boundary method for hyperbolic conservation laws

by: Phillip Colella, Daniel T Graves, Benjamin J Keen, David Modiano

Journal of Computational Physics, Vol. 211, No. 1. (1 January 2006), pp. 347-366.

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Abstract

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 L1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.

@article{citeulike:1627923, abstract = {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 L1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.}, author = {Colella, Phillip and Graves, Daniel T. and Keen, Benjamin J. and Modiano, David }, citeulike-article-id = {1627923}, doi = {http://dx.doi.org/10.1016/j.jcp.2005.05.026}, journal = {Journal of Computational Physics}, keywords = {pde}, month = {January}, number = {1}, pages = {347--366}, posted-at = {2007-09-06 16:08:57}, priority = {4}, title = {A Cartesian grid embedded boundary method for hyperbolic conservation laws}, url = {http://dx.doi.org/10.1016/j.jcp.2005.05.026}, volume = {211}, year = {2006} }

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TY - JOUR ID - citeulike:1627923 L3 - citeulike-article-id:1627923 TI - A Cartesian grid embedded boundary method for hyperbolic conservation laws JF - Journal of Computational Physics VL - 211 IS - 1 SP - 347 EP - 366 N2 - 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 L1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary. KW - pde AU - Colella, Phillip AU - Graves, Daniel AU - Keen, Benjamin AU - Modiano, David PY - 2006/01/01/ UR - http://dx.doi.org/10.1016/j.jcp.2005.05.026 ER -

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