A Cartesian grid embedded boundary method for hyperbolic conservation laws |
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| Institution: | 1. Lawrence Berkeley National Laboratory, Applied Numerical Algorithms Group, MS 50A-1148, 1 Cyclotron Road, Berkeley, CA 94720, United States;2. Mathematics Department, University of Michigan, Ann Arbor, MI, United States;1. Aerothermodynamics Branch, Research Directorate, NASA Langley Research Center, Hampton, VA 23681, USA;2. Division of Applied Mathematics, Brown University, Providence, RI 02912, USA;3. INRIA Bordeaux Sud-Ouest, Laboratoire de Mathématiques et de leurs applications Bâtiment IPRA, Universite de Pau et des Pays de l''Adour, 64013 Pau Cedex, France |
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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. |
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