99-05

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

by John,V.; Layton,W.J.

 

Preprint series: 99-05, Preprints

The paper is published: Computing 66, 269 - 287, 2001 with the title \' Approximating Local Averages of Fluid Velocities: The Stokes Problem\'

MSC:
65N15 Error bounds
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
76D07 Stokes 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


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