ON AN IMPLICIT ENO SCHEME

Essentially non-oscillatory (ENO) schemes, which have high order accur acy in regions where solutions are smooth and effectively ca ptu re sh ocks a nd discontinuities, have been developed for numerical solution of hyperbolic equations. These methods have traditionally been impleme nted using explicit Euler or explicit Runge-Kutta time marching scheme s and consequently suffer from the Courant-Friedrichs-Lewy (CFL) time step restriction. This restriction is significant for steady-state pro blems and for transient problems with fronts whose speed is slow compa red to the propagation speed in the rest of the domain. In this paper, a novel implicit time marching implementation of the ENO-Roe scheme i s developed. Simulation results which demonstrate the benefits of this implicit implementation are presented. (C) 1994 Academic Press, Inc.