A LARGE TIME STEP GENERALIZATION OF GODUNOV METHOD FOR SYSTEMS OF CONSERVATION-LAWS

A generalization of S. K. Godunov's method for solving systems of conservation laws is proposed which can be applied for arbitrarily large time steps. Interactions of waves from neighboring Riemann problems are handled in an approximate but conservative manner that is exact for linear problems. For nonlinear systems it is found that better accuracy and sharper resolution of discontinuities is often obtained with Courant numbers somewhat larger than those allowed in Godunov's method. We explore the reasons for this behavior and, more generally, the effects of approximating wave interactions linearly. This linearization is easy to implement and may also be useful in other contexts, such as mesh refinement or shock tracking. A large time step generalization of the random choice method is also mentioned.