Contributed Talk
Maximum principle preserving space and time flux limiting
King Abdullah University of Science & Technology, Saudi Arabia
Abstract
I will present a framework for enforcing maximum (or minimum) bounds on the solution of a scalar conservation law including both hyperbolic and diffusive terms. The method can be used to achieve arbitrarily high order accuracy in time and space, thus providing a way to get past the well-known order barriers for SSP time discretizations. The approach is based on combining a high-order almost-bound-preserving solution with a first-order bound-preserving solution through a novel limiting technique. I will show examples using WENO finite volume methods in space and high-order extrapolation Runge-Kutta methods in time. If there is time I will show preliminary results of applying the same technique to preserve positivity for the shallow water equations.