On Simulating Flows with Multiple Time Scales Using a Method of Averages

Abstract.

We present a new method, based on averaging, to simulate certain systems with multiple time scales efficiently and demonstrate its utility in the context of the shallow-water equations. We first develop the method in a simple linear setting and analytically prove its stability. This is followed by an extension to the full equations and a presentation of a computational model for it. In this preliminary study, we find that the new method produces results that are very close to a fully explicit (spatially and temporally) second-order accurate scheme and much better than a fully explicit (spatially and temporally) first-order accurate scheme, while costing less than the first-order accurate scheme.