Analysis of numerical errors in large eddy simulation

Abstract

We consider the question of "numerical errors" in large eddy simulation. It is often claimed that straightforward discretization and solution using centered methods of models for large eddy motion can simulate the motion of turbulent flows with complexity independent of the Reynolds number and dependence only on the resolution "δ" of the eddies sought. This report considers this question analytically: Is it possible to prove error estimates for discretizations of actually used large eddy models whose error constants depend only on δ but not Re? We consider the most common, simplest, and most mathematically tractable model and the most mathematically clear discretization. In two cases, we prove such an error estimate and try to explain why our technique of proof fails in the most general case. Our analysis aims to assume as little time regularity on the true solution as possible.