A Second-Order Godunov Method on Arbitrary Grids

generalized algorithm. The previous high order Godunov methods on which it is strongly based can be found in the A second-order Godunov method is proposed for the solution of general systems of conservation laws on arbitrary grids. Some original bibliography ([2, 4, 14, 15]) and in the book of applications are discussed: moving and deforming grids, local grid LeVecque [8]. refinement, Lagrangian grids that make contact discontinuities perIn the second section we introduce a rigorous secondfectly sharp, and a new way to solve the time dependent small order accurate way of solving the generalized Riemann disturbance transonic flow equations of gas dynamics. As part of problem for arbitrary systems of conservation laws. This the algorithm, a way is presented to solve generalized Riemann problems with second-order accuracy. � 1996 Academic Press, Inc. is a tool required by all high order Godunov methods; the algorithm presented here is quite general and conceptually simple. INTRODUCTION