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Convergence Analysis of a Fully Discrete Family of Iterated Deconvolution Methods for Turbulence Modeling with Time Relaxation

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Ingram, R. and Manica, C. C. and Mays, N. and Stanculescu, I. (2012) Convergence Analysis of a Fully Discrete Family of Iterated Deconvolution Methods for Turbulence Modeling with Time Relaxation. Advances in Numerical Analysis, 2012. pp. 1-32. ISSN 1687-9562

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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.


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Details

Item Type: Article
Status: Published
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Ingram, R.
Manica, C. C.
Mays, N.nmays@wju.edu
Stanculescu, I.
Date: 2012
Date Type: Publication
Journal or Publication Title: Advances in Numerical Analysis
Volume: 2012
Publisher: Hindawi
Page Range: pp. 1-32
DOI or Unique Handle: 10.1155/2012/162539
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Refereed: No
ISSN: 1687-9562
Official URL: https://www.hindawi.com/journals/ana/2012/162539/
Article Type: Research Article
Date Deposited: 12 May 2020 15:05
Last Modified: 12 May 2020 15:05
URI: http://d-scholarship.pitt.edu/id/eprint/38843

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