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A 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. This thesis gives an extension of the kinetic scheme for gas dynamics by Perthame [SIAM J. Num. Anal., 27:1305–1421] on arbitrary Cartesian meshes. The formulation allows a time step based only on the underlying regular cell size, and retains L1 -stability, positivity and second order convergence. Numerical convergence studies on irregular grids in one and two space dimensions are presented.