ACCURATE MONOTONICITY-PRESERVING SCHEMES WITH RUNGE-KUTTA TIME-STEPPING

A new class of high-order monotonicity-preserving schemes for the nume rical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynomial rec onstruction. The limiting is designed to preserve accuracy near extrem a and to work well with Runge-Kutta time stepping. Computational effic iency is enhanced by a simple test that determines whether the limitin g procedure is needed. For linear advection in one dimension, these sc hemes are shown to be monotonicity-preserving and uniformly high-order accurate. Numerical experiments for advection as well as the Euler eq uations also confirm their high accuracy, good shock resolution, and c omputational efficiency. (C) 1997 Academic Press.