Seminar in Numerical Analysis: Valeriu Savcenco (Shell Global Solutions/ TU Eindhoven)

Analysis of explicit multirate Runge-Kutta schemes for conservation laws

Multirate methods are highly efficient for large-scale ODE and PDE problems with widely different time scales. Multirate methods enable one to use large time steps for slowly varying spatial regions, and small steps for rapidly varying spatial regions. Multirate schemes for conservation laws seem to come in two flavors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this presentation these two defects will be discussed for one-dimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total variation diminishing (TVD) property. The study of these properties will be done within the framework of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for genuine multirate schemes, but not for general partitioned methods.

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