Workshop on Numerical Methods and Analysis in CFD - Abstract

Ern, Alexandre

A new perspective on time-stepping schemes: Beyond strong stability

We introduce a technique that makes every explicit Runge--Kutta time stepping method invariant-domain preserving when applied to high-order discretizations of the Cauchy problem associated with nonlinear conservation equations. The main advantage over the popular strong stability preserving (SSP) paradigm is more flexibility in the choice of the ERK scheme, thus allowing for a less stringent restriction on the time step and circumventing order barriers. The technique is agnostic to the space discretization. In a second step, we extend the technique to implicit-explicit (IMEX) time-stepping schemes for the Cauchy problem where the evolution operator comprises a hyperbolic part and a parabolic part with diffusion and stiff relaxation terms. Numerical experiments are presented to illustrate the theory.
This is joint work with J.-L. Guermond (Texas A&M).