A second order kinetic scheme for gas dynamics on arbitrary grids

  • Authors:

  • Benjamin Keen;Smadar Karni

  • Affiliations:

  • Department of Mathematics, University of Michigan, 525 E. University Avenue, Room 2074, Ann Arbor, MI 48109-1109, USA and IDA Center for Computing Sciences, 17100 Science Drive Bowie, MD 20715, US ...;Department of Mathematics, University of Michigan, 525 E. University Avenue, Room 2074, Ann Arbor, MI 48109-1109, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

Cartesian meshes for domains with complicated boundaries give rise to cut cells with arbitrarily small volumes. Explicit integration schemes over such meshes have a time step restriction proportional to the smallest cell volume. We present an implementation of the kinetic scheme for gas dynamics by Perthame [B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property. SIAM J. Num. Anal. 27 (1990) 1405-1421] on arbitrary Cartesian meshes. The formulation allows a time step based on the underlying regular cell size, and retains L"1-stability, positivity and second order convergence. Numerical convergence studies on arbitrary grids are presented.