Numerical Experiments with the Osher Upwind Scheme for the Euler Equations

Abstract

The Osher algorithm for solving the Euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations. A first-order accurate version of the numerical method was derived by Osher circa 1980 for the one-dimensional non-isentropic Euler equations in Cartesian coordinates. In this paper, the extension of the scheme to arbitrary two-dimensional geometries is explained. Results are then presented for several example problems in one and two dimensions. Future work will include extension of the method to second-order accuracy and the development of implicit time differencing for the Osher algorithm.