State vector splitting: a numerical scheme for the Euler equations

Abstract

A new numerical scheme was developed for the solution of the Euler equations in multi-dimensions. The scheme removes the critical dependency on the choice of a "good" grid by making use of the multidimensional character of the Euler Equations. In addition, a new procedure for implementing solid wall boundary conditions was introduced which does not require body-fitted grids. This grid independent nature of the scheme allows one to solve complicated geometry problems on simple regular grids. The scheme uses an upwind direction which is independent of the underlying coordinate system. This direction is determined only by the local state of the fluid. The scheme is explicit and easy to implement for both serial and parallel computation. The current implementation of the algorithm for two space dimensions can handle unsteady fows around almost arbitrary geometries using a simple cartesian mesh. Several numerical experiments have been done to show the flexibility and the robust- ness of the algorithm.