A second order kinetic scheme for gas dynamics on arbitrary grids

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 L1-stability, positivity and second order convergence. Numerical convergence studies on arbitrary grids are presented.