THE RELAXATION SCHEMES FOR SYSTEMS OF CONSERVATION-LAWS IN ARBITRARY SPACE DIMENSIONS

We present a class of numerical schemes (called the relaxation schemes ) for systems of conservation laws in several space dimensions. The id ea is to use a local relaxation approximation. We construct a linear h yperbolic system with a stiff lower order term that approximates the o riginal system with a small dissipative correction. The new system can be served by underresolved stable numerical discretizations without u sing either Riemann solvers spatially or a nonlinear system of algebra ic equations solvers temporally. Numerical results for 1-D and 2-D pro blems are presented. The second-order schemes are shown to be total va riation diminishing (TVD) in the zero relaxation limit for scalar equa tions. (C) 1995 John Wiley & Sons, Inc.