Computational Turbulent Incompressible Flow: Applied Mathematics: Body and Soul 4 / Edition 1

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This is Volume 4 of the book series of the Body and Soul mathematics education reform program. It presents a unified new approach to computational simulation of turbulent flow starting from the general basis of calculus and linear algebra of Vol 1-3. The book puts the Body and Soul computational finite element methodology in the form of General Galerkin (G2) up against the challenge of computing turbulent solutions of the inviscid Euler equations and the Navier-Stokes equations with small viscosity. This is an outstanding textbook presenting plenty of new material with an excellent pedagogical approach.

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Editorial Reviews

From the Publisher
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)

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Product Details

  • ISBN-13: 9783540465317
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 2/21/2007
  • Series: Applied Mathematics: Body and Soul Series
  • Edition description: 2007
  • Edition number: 1
  • Pages: 401
  • Product dimensions: 6.10 (w) x 9.40 (h) x 0.80 (d)

Meet the Author

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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Table of Contents

I Overview.- 1 Main Objective.- 2 Mysteries and Secrets.- 3 Turbulent Flow and History of Aviation.- 4 The Euler Equations.- 5 The Incompressible Euler and Navier-Stokes Equations.- 6 Triumph and Failure of Mathematics.- 7 Laminar and Turbulent Flow.- 8 Computational Turbulence.- 9 A First Study of Stability.- 10 d'Alembert's Mystery and Bernoulli's Law.- 11 Prandtl's Resolution of d'Alemberts's Mystery.- 12 New Resolution of d'Almenbert's Mystery.- II Mathematics of Turbulence.- 13 Turbulence and Chaos.- 14 A $1 Million Prize Problem.- 15 Work Uniqueness by Computation.- 16 Existence of e-Weak Solutions by G2.- 17 Stability Aspects of Turbulence in Model Problems.- 18 A Convection-Diffusion Model Problem.- 19 G2 for Euler.- 20 Summary of Mathematical Aspects.- III Secrets.- 21 Secrets of Ball Sports.- 22 Secrets of Flight.- 23 Secrets of Sailing.- 35 Secrets of Racing.- IV Computational Method.- 25 Reynolds Stresses In and Out.- 26 Smagorinsky Viscosity In and Out.- 27 Friction Boundary Condition as Wall Model.- 28 G2 for Navier-Stokes Equations.- 29 A Discrete Solver.- 30 G2 as Adaptive DNS/LES.- 31 Implementation of G2 with FEniCS.- 32 Moving Meshes adn ALE Methods.- V Flow Fundamentals.- 33 Bluff Body Flow.- 34 Boundary Layers.- 35 Separation.- 36 Transition to Turbulence.- VI Loschmidt's Mystery.- 37 Thermodynamics.- 38 Joule's 1845 Experiment.- 39 Compressible Euler in 1d.- 40 Burgers' Equation.- 41 Compressible Euler in 3d.- 42 EG2 for Compressible Flow.- 43 Philosophy of EG2.- 44 Does God Really Play Dice?- References.- Index

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