Time step selection for shock problems

Abstract

AbstractThe solution to a conservation law is integrated in time by an explicit embedded Runge–Kutta method. The time steps are chosen so that a bound on the local error is satisfied. At discontinuities such as shocks in the solution the time step is too pessimistic. By filtering the error estimate the time steps are determined by the smooth parts of the solution. The technique is justified theoretically and in numerical experiments. Copyright © 2001 John Wiley & Sons, Ltd.