A Cartesian grid embedded boundary method for hyperbolic conservation laws

  • Authors:

  • Phillip Colella;Daniel T. Graves;Benjamin J. Keen;David Modiano

  • Affiliations:

  • Lawrence Berkeley National Laboratory, Applied Numerical Algorithms Group, MS 50A-1148, 1 Cyclotron Road, Berkeley, CA 94720, United States;Lawrence Berkeley National Laboratory, Applied Numerical Algorithms Group, MS 50A-1148, 1 Cyclotron Road, Berkeley, CA 94720, United States;Mathematics Department, University of Michigan, Ann Arbor, MI, United States;Lawrence Berkeley National Laboratory, Applied Numerical Algorithms Group, MS 50A-1148, 1 Cyclotron Road, Berkeley, CA 94720, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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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 L^1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.