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.
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