Accurate monotonicity-preserving schemes with Runge-Kutta time stepping

[摘要] A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynomial reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown to be monotonicity-preserving and uniformly high-order accurate. Numerical experiments for advection as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency. (C) 1997 Academic Press.

[发布日期] 1997-09-01