ON SIMULATING FLOWS WITH MULTIPLE TIME SCALES USING A METHOD OF AVERAGES

We present a new method, based on averaging, to simulate certain syste ms with multiple time scales efficiently and demonstrate its utility i n the context of the shallow-water equations. We first develop the met hod in a simple linear setting and analytically prove its stability. T his is followed by an extension to the full equations and a presentati on 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 e xplicit (spatially and temporally) second-order accurate scheme and mu ch better than a fully explicit (spatially and temporally) first-order accurate scheme, while costing less than the first-order accurate sch eme.