Computational Turbulent Incompressible Flow

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.

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].

Outstanding textbook presenting plenty of new material Excellent pedagogical approach Includes supplementary material: sn.pub/extras

Autorentext

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

  Klappentext

This is Volume 4 of the book series of the Body & Soul mathematics education reform program, and 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 & 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.
The book shows that direct application of G2 without any turbulence or wall modeling, allows reliable computation on a PC of mean value quantities of turbulent flow such as drag and lift.
The power of G2 is demonstrated by resolving several classical scientific paradoxes of fluid flow and by uncovering secrets of flying, sailing, racing and ball sports. The book presents new aspects on both mathematics and computation of turbulent flow, and challenges established approaches.

The book is directed to a wide audience of computational mathematicians fluid dynamicists and scientists.

The G2 solver is available as part the free software project FEniCS at www.fenics.org. The book has a dedicated dynamic web page, including movies from a wide variety of simulations, at www.bodysoulmath.org.

The book is focussed on incompressible flow, but opens to compressible flow continued in Vol 5 on thermodynamics.

The authors are experts on computational mathematics and technology.

Inhalt
Overview.- Main Objective.- Mysteries and Secrets.- Turbulent Flow and History of Aviation.- The Euler Equations.- The Incompressible Euler and NavierStokes Equations.- Triumph and Failure of Mathematics.- Laminar and Turbulent Flow.- Computational Turbulence.- A First Study of Stability.- d'Alembert's Mystery and Bernoulli's Law.- Prandtl's Resolution of d'Alembert's Mystery.- New Resolution of d'Alembert's Mystery.- Mathematics of Turbulence.- Turbulence and Chaos.- A $1 Million Prize Problem.- Weak Uniqueness by Computation.- Existence of ?-Weak Solutions by G2.- Stability Aspects of Turbulence in Model Problems.- A Convection-Diffusion Model Problem.- G2 for Euler.- Summary of Mathematical Aspects.- Secrets.- Secrets of Ball Sports.- Secrets of Flight.- Secrets of Sailing.- Secrets of Racing.- Computational Method.- Reynolds Stresses In and Out.- Smagorinsky Viscosity In and Out.- Friction Boundary Condition as Wall Model.- G2 for Navier-Stokes Equations.- A Discrete Solver.- G2 as Adaptive DNS/LES.- Implementation of G2 with FEniCS.- Moving Meshes and ALE Methods.- Flow Fundamentals.- Bluff Body Flow.- Boundary Layers.- Separation.- Transition to Turbulence.- Loschmidt's Mystery.- Thermodynamics.- Joule's 1845 Experiment.- Compressible Euler in 1d.- Burgers' Equation.- Compressible Euler in 3d.- EG2 for Compressible Flow.- Philosophy of EG2.- Does God Really Play Dice?.