Multilevel methods for the simulation of turbulence. A simple model

Our aim in this article is to present for a very simple model-namely a pair of ordinary coupled differential equations-some of the features of the multilevel numerical methods which have been introduced recently for the numerical simulation of turbulent flows. The two components of this simple differential system are intended to represent the large and small scale components of a flow. We show that many new numerical schemes can be introduced by treating differently the small and large scale components; also different time steps can be used for these two components. The stability analysis which we conduct for this simple model shows that these new multilevel schemes can produce a substantial saving in computing time, although the stability analysis leads sometime to counterintuitive conclusions. The error analysis for this model will be conducted elsewhere. Also the reader is referred to the articles quoted below for the utilization of similar multilevel schemes for the Navier-Stokes equations themselves. 32 refs., 6 figs