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Full Description
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].
Contents
Overview.- Main Objective.- Mysteries and Secrets.- Turbulent Flow and History of Aviation.- The Euler Equations.- The Incompressible Euler and Navier-Stokes 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?.
