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Approximate Deconvolution Models of Turbulence

Analysis, Phenomenology and Numerical Analysis

  • Book
  • © 2012

Overview

Authors:
  1. William J. Layton

    1. Dept. Mathematics, University of Pittsburgh, Pittsburgh, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Leo Rebholz

    1. Department of Mathematical Sciences, Clemson University, Clemson, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Comprehensive treatment of the subject including modeling, analysis, phenomenology and numerical analysis
  • Includes both turbulence models and Navier-Stokes regularizations
  • Presents current state of the models and indicates important questions for further development

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2042)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • William J. Layton, Leo G. Rebholz
    Pages 1-33

  3. Large Eddy Simulation

    • William J. Layton, Leo G. Rebholz
    Pages 35-60

  4. Approximate Deconvolution Operators and Models

    • William J. Layton, Leo G. Rebholz
    Pages 61-88

  5. Phenomenology of ADMs

    • William J. Layton, Leo G. Rebholz
    Pages 89-97

  6. Time Relaxation Truncates Scales

    • William J. Layton, Leo G. Rebholz
    Pages 99-120

  7. The Leray-Deconvolution Regularization

    • William J. Layton, Leo G. Rebholz
    Pages 121-144

  8. NS-Alpha- and NS-Omega-Deconvolution Regularizations

    • William J. Layton, Leo G. Rebholz
    Pages 145-162

  9. Back Matter

    Pages 163-184
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Keywords

About this book

This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting Approximate Deconvolution Models or ADMs have some advantages over more commonly used turbulence models – as well as some disadvantages. Our goal in this book is to provide a clear and complete mathematical development of ADMs, while pointing out the difficulties that remain. In order to do so, we present the analytical theory of ADMs, along with its connections, motivations and complements in the phenomenology of and algorithms for ADMs.

Reviews

From the reviews:

“This monograph presents a mathematical approach to turbulence modeling and is aimed at graduate students and researchers in the field of computational fluid dynamics. … The book presents the governing Navier-Stokes equations and the basics of large eddy simulation from a mathematical perspective without going into details of the flow physics. … Difficulties of the models in the vicinity of walls with no-slip boundary conditions are mentioned, and numerical examples of different flows illustrate some properties of the approximate deconvolution models.” (Kai Schneider, Zentralblatt MATH, Vol. 1241, 2012)

Authors and Affiliations

  • Dept. Mathematics, University of Pittsburgh, Pittsburgh, USA

    William J. Layton

  • Department of Mathematical Sciences, Clemson University, Clemson, USA

    Leo Rebholz

Bibliographic Information

  • Book Title: Approximate Deconvolution Models of Turbulence

  • Book Subtitle: Analysis, Phenomenology and Numerical Analysis

  • Authors: William J. Layton, Leo Rebholz

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-24409-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2012

  • Softcover ISBN: 978-3-642-24408-7Published: 07 January 2012

  • eBook ISBN: 978-3-642-24409-4Published: 06 January 2012

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 184

  • Number of Illustrations: 11 b/w illustrations, 11 illustrations in colour

  • Topics: Numerical Analysis, Engineering Fluid Dynamics

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