Computational Turbulent Incompressible Flow

1. Front Matter

   Pages I-XIX

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2. Overview

   1. Front Matter

      Pages 1-1

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   2. Main Objective

      Pages 3-28

   3. Mysteries and Secrets

      Pages 29-32

   4. Turbulent Flow and History of Aviation

      Pages 33-37

   5. The Euler Equations

      Pages 39-42

   6. The Incompressible Euler and Navier–Stokes Equations

      Pages 43-47

   7. Triumph and Failure of Mathematics

      Pages 49-50

   8. Laminar and Turbulent Flow

      Pages 51-55

   9. Computational Turbulence

      Pages 57-63

   10. A First Study of Stability

       Pages 65-71

   11. d'Alembert's Mystery and Bernoulli's Law

       Pages 73-79

   12. Prandtl's Resolution of d'Alembert's Mystery

       Pages 81-85

   13. New Resolution of d'Alembert's Mystery

       Pages 87-94

3. Mathematics of Turbulence

   1. Front Matter

      Pages 96-96

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   2. Turbulence and Chaos

      Pages 97-111

   3. A $1 Million Prize Problem

      Pages 113-122

   4. Weak Uniqueness by Computation

      Pages 123-130

   5. Existence of ε-Weak Solutions by G2

      Pages 131-135

   6. Stability Aspects of Turbulence in Model Problems

      Pages 137-145

Applied Mathematics: Body&Soul is a mathematics education reform p- gram including a series of books, together with associated educational ma- rial and open source software freely available from the project web page at www.bodysoulmath.org. Body&Soul re?ects the revolutionary new possibilities of mathematical modeling opened by the modern computer in the form of Computational C- culus (CC), which is now changing the paradigm of mathematical modeling in science and technology with new methods, questions and answers, as a modern form of the classical calculus of Leibniz and Newton. The Body&Soul series of books presents CC in a synthesis of com- tational mathematics (Body) and analytical mathematics (Soul) including applications. Volumes 1-3 [36] give a modern version of calculus and linear algebra including computation starting at a basic undergraduate level, and subsequent volumes on a graduate level cover di?erent areas of applications with focus on computational methods: • Volume 4: Computational Turbulent Incompressible Flow. • Volume 5: Computational Thermodynamics. • Volume 6: Computational Dynamical Systems. The present book is Volume 4, with Volumes 5 and 6 to appear in 2007 and further volumes on solid mechanics and electro-magnetics being planned. A gentle introduction to the Body&Soul series is given in [63].

• Navier-Stokes equation
• Navier–Stokes equation
• chaos
• computational mathematics
• convection
• fluid dynamics
• simulation

From the reviews:

"This book considers the numerical simulation of incompressible turbulent flows which are modeled by the Euler equations or the Navier-Stokes equations. … Throughout the book, a lot of numerical examples are presented. … they might be used in courses to illustrate the features of turbulent flows for students." (John Volker, Mathematical Reviews, Issue 2008 d)

• School of Computer Science and Communication, Royal Institute of Technology - KTH, Sweden

  Johan Hoffman

• School of Engineering Sciences, Royal Institute of Technology-KTH, Sweden

  Claes Johnson

The authors are leading researchers in computational mathematics who have written various successful books.

The authors have been awarded several prizes:

• Johan Hoffman: Bill Morton Prize, Leslie Fox Prize
• Claes Johnson: Humboldt Research Prize

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