A second order kinetic scheme for gas dynamics on arbitrary grids
Journal of Computational Physics
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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.