by Dunca, A., John, V., Layton, W..

**Series:** 2002-29, Preprints

- MSC:
- 65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

**Abstract:**

In the approximation of higher Reynolds number flow problems, the usual

approach is to seek to approximate suitable velocity averages rather than

the pointwise fluid velocity itself. We consider an approach to this

question wherein the averages are local, spatial averages computed with

the Gaussian filter (as in large eddy simulation) and the averages

are approximated without using either turbulent closure models or

wall laws. The approach we consider is a (underresolved) direct

numerical simulation followed by postprocessing to extract accurate

flow averages. \'A priori and a posteriori

estimates are given for $\| g_\delta\ast(\bu-\bu^h)\|_0$

which can give guidance for the coupling between the averaging radius

$\delta$ and the mesh width $h$. Numerical experiments support the

error estimates and illustrate the adaptive grid refinement procedure.

**Keywords:**

large eddy simulation, postprocessing, convergence of the finite element method