A Second Order Kinetic Scheme for Gas Dynamics on Arbitrary Grids

Benjamin Keen, University of Michigan

Cartesian mesh discretizations of complicated geometries lead to arbitrarily small cell sizes. For hyperbolic systems, this leads an unacceptable CFL stability restriction on the timestep without modifying the underlying numerical scheme.

This is a new method of overcoming this so-called ‘small cell problem’. It is specifically for the Euler equations of gas dynamics, and is based on a modification of a kinetic scheme. The original scheme is positive, L_1 stable, and second order; as reformulated to work in the presence of small cells these properties are shown to remain. Numerical examples and convergence tests are provided.

Abstract Author(s): Benjamin Keen