Mathematics Faculty Articles

Title

Numerical Analysis of Leray-Tikhonov Deconvolution Models of Fluid Motion

Document Type

Article

Publication Date

9-1-2010

Publication Title

Computers & Mathematics with Applications

Keywords

Navier-Stokes equation, Leray deconvolution, Tikhonov regularization, Turbulence models

ISSN

0898-1221

Volume

60

Issue/No.

5

First Page

1440

Last Page

1456

Abstract

This report develops and studies a new family of Navier–Stokes equation regularizations: Leray–Tikhonov regularizations with time relaxation models. This new family of turbulence models is based on a modification (consistent with the large scales) of Tikhonov–Lavrentiev regularization. With this approach, we obtain an approximation of the unfiltered solution by one filtering step. We introduce the modified Tikhonov deconvolution operator and study its mathematical properties. We also perform rigorous numerical analysis of a computationally attractive algorithm for this family of models and present numerical experiments using it

DOI

10.1016/j.camwa.2010.06.026

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Peer Reviewed

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