Abstract: A High resolution and high order accurate upwind scheme is presented for solving Euler equations on unstructured meshes. The spatial discretization is accomplished by a cell centered finite volume formulation using Roes characteristic based flux difference splitting.High order accuracy is achieved by a multidimensional linear reconstruction process. Solutions are advanced in time by a four stage Runge Kutta time stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. This approach ensures good shock capturing properties and produces sharp tangential discontinuities without oscillations. Numerical examples to illustrate the performance of the proposed schemes are given.

Key words: Euler equation of motion grid generation(mathematic), finite volume theory Runge-Kutta method