COMPOSITE SCHEMES FOR CONSERVATION-LAWS

Global composition of several time steps of the two-step Lax-Wendroff scheme followed by a Lax-Friedrichs step seems to enhance the best fea tures of both, although it is only first order accurate. We show this by means of some examples of one-dimensional shallow water flow over a n obstacle. In two dimensions we present a new version of Lax-Friedric hs and an associated second order predictor-corrector method. Composit ion of these schemes is shown to be effective and efficient for some t wo-dimensional Riemann problems and for Noh's infinite strength cylind rical shock problem. We also show comparable results for composition o f the predictor-corrector scheme with a modified second order accurate weighted essentially nonoscillatory (WENO) scheme. That composition i s second order but is more efficient and has better symmetry propertie s than WENO alone. For scalar advection in two dimensions the optimal stability of the new predictor-corrector scheme is shown using compute r algebra. We also show that the generalization of this scheme to thre e dimensions is unstable, but by using sampling we are able to show th at the composites are suboptimally stable.