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

Richard Ingram | Zendy; Carolina C. Manica | Zendy; Nicholas Mays | Zendy; Iuliana Stanculescu | Zendy

Open Access

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

Author(s) -

Richard Ingram,

Carolina C. Manica,

Nicholas Mays,

Iuliana Stanculescu

Publication year - 2012

Publication title -

advances in numerical analysis

Language(s) - English

Resource type - Journals

eISSN - 1687-9570

pISSN - 1687-9562

DOI - 10.1155/2012/162539

Subject(s) - iterated function , tikhonov regularization , deconvolution , mathematics , regularization (linguistics) , operator (biology) , convergence (economics) , relaxation (psychology) , mathematical analysis , mathematical optimization , inverse problem , algorithm , computer science , psychology , social psychology , biochemistry , chemistry , repressor , artificial intelligence , transcription factor , economics , gene , economic growth

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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