### 1999-05

#### Approximation of the Larger Eddies in Fluid Motion, I: Direct Simulation for the Stokes Problem

Series: 1999-05, Preprints

MSC:
65N15 Error bounds
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
76D07 Stokes and related (Oseen, etc.) flows

Abstract:
As a first step to developing mathematical support for finite element
approximation to the large eddies in fluid motion we consider herein the Stokes
problem. We show that the local average of the usual approximate flow field
$\1^h$ over radius $\delta$ provides a very accurate approximation to the flow
structures of $O(\delta)$ or greater. The extra accuracy appears for quadratic
or higher velocity elements and degrades to the usual finite element accuracy
as the averaging radius $\delta \rightarrow h$ (the local meshwidth). We give
both \'a priori and a posteriori error estimates incorporating this effect.

Keywords:
large eddy simulation, finite element method, computational fluid dynamics

This paper was published in:
Computing 66,