Mathematics Faculty Articles

Document Type

Article

Publication Date

7-25-2012

Publication Title

Advances in Numerical Analysis

ISSN

1687-9562

Volume

2012

Issue/No.

2012

First Page

32pp

Abstract

We present a general theory for regularization models of the Navier-Stokes equations based on the Leray deconvolution model with a general deconvolution operator designed to fit a few important key properties. We provide examples of this type of operator, such as the (modified) Tikhonov-Lavrentiev and (modified) Iterated Tikhonov-Lavrentiev operators, and study their mathematical properties. An existence theory is derived for the family of models and a rigorous convergence theory is derived for the resulting algorithms. Our theoretical results are supported by numerical testing with the Taylor-Green vortex problem, presented for the special operator cases mentioned above.

Comments

Copyright © 2012 R. Ingram et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

DOI

10.1155/2012/162539

Peer Reviewed

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