The Osher Upwind Scheme and its Application to Cosmic Gas Dynamics

Abstract

Details of the second order Osher scheme for the multi-dimensional Euler equation are presented. The adopted method to attain the second order of accuracy differs from the existing second order formulation by Osher. The present method is easy to be implemented and can be applied to other first order upwind schemes. Two types of numerical integration forms are coded. One is written in the integral form (cell method), and the other is the usual finite-difference form. Both forms work well and can capture strong shocks without any auxiliary artificial damping. The integration form strictly satisfies the flux conservation even on geometrical singular coordinate lines, which inevitably appear in three dimensional calculations with bodies embedded. Hydrodynamic calculations of the interaction between a stellar wind and an accretion flow are performed to demonstrate the ability of the present method.