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An Introduction to Computational Fluid Mechanics by Example, 2nd Edition

ISBN: 978-0-470-91517-2
320 pages
March 2011
An Introduction to Computational Fluid Mechanics by Example, 2nd Edition (047091517X) cover image


This new book builds on the original classic textbook entitled: An Introduction to Computational Fluid Mechanics by C. Y. Chow which was originally published in 1979. In the decades that have passed since this book was published the field of computational fluid dynamics has seen a number of changes in both the sophistication of the algorithms used but also advances in the computer hardware and software available. This new book incorporates the latest algorithms in the solution techniques and supports this by using numerous examples of applications to a broad range of industries from mechanical and aerospace disciplines to civil and the biosciences. The computer programs are developed and available in MATLAB. In addition the core text provides up-to-date solution methods for the Navier-Stokes equations, including fractional step time-advancement, and pseudo-spectral methods. The computer codes at the following website: www.wiley.com/go/biringen
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Table of Contents

Preface ix

1 Flow Topics Governed by Ordinary Differential Equations: Initial-Value Problems 1

1.1 Numerical Solution of Ordinary Differential Equations: Initial-Value Problems  1

1.2 Free Falling of a Spherical Body  5

1.3 Computer Simulation of Some Restrained Motions  13

1.4 Fourth-Order Runge-Kutta Method for Computing Two-Dimensional Motions of a Body through a Fluid  22

1.5 Ballistics of a Spherical Projectile  24

1.6 Flight Path of a Glider—A Graphical Presentation  32

1.7 Rolling Up of the Trailing Vortex Sheet behind a Finite Wing  35

Appendix  44

2 Inviscid Fluid Flows 50

2.1 Incompressible Potential Flows  51

2.2 Numerical Solution of Second-Order Ordinary Differential Equations: Boundary-Value Problems  55

2.3 Radial Flow Caused by Distributed Sources and Sinks  60

2.4 Inverse Method I: Superposition of Elementary Flows  61

2.5 von Kármán’s Method for Approximating Flow Past Bodies of Revolution  69

2.6 Inverse Method II: Conformal Mapping  76

2.7 Classification of Second-Order Partial Differential Equations  87

2.8 Numerical Methods for Solving Elliptic Partial Differential Equations  90

2.9 Potential Flows in Ducts or around Bodies—Irregular and Derivative Boundary Conditions  96

2.10 Numerical Solution of Hyperbolic Partial Differential Equations  105

2.11 Propagation and Reflection of a Small-Amplitude Wave  110

2.12 Propagation of a Finite-Amplitude Wave: Formation of a Shock  120

2.13 An Application to Biological Fluid Dynamics: Flow in an Elastic Tube  128

Appendix  143

3 Viscous Fluid Flows 145

3.1 Governing Equations for Viscous Flows  145

3.2 Self-Similar Laminar Boundary-Layer Flows  147

3.3 Flat-Plate Thermometer Problem—Ordinary Boundary-Value Problems Involving Derivative Boundary Conditions  157

3.4 Pipe and Open-Channel Flows  163

3.5 Explicit Methods for Solving Parabolic Partial Differential Equations—Generalized Rayleigh Problem  168

3.6 Implicit Methods for Solving Parabolic Partial Differential Equations—Starting Flow in a Channel  173

3.7 Numerical Solution of Biharmonic Equations—Stokes Flows  179

3.8 Flow Stability and Pseudo-Spectral Methods  185

Appendix  207

4 Numerical Solution of the Incompressible Navier-Stokes Equation 215

4.1 Flow around a Sphere at Finite Reynolds Numbers—Galerkin Method  216

4.2 Upwind Differencing and Artificial Viscosity  229

4.3 Bénard and Taylor Instabilities  234

4.4 Primitive Variable Formulation: Algorithmic Considerations  249

4.5 Primitive Variable Formulation: Numerical Integration of the Navier-Stokes Equation  258

4.6 Flow Past a Circular Cylinder: An Example for the

Vorticity-Stream Function Formulation  280

Appendix  297

Bibliography 298

Index 303

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Author Information

Dr. Sedat Biringen is a Professor of Aerospace Engineering Sciences at the University of Colorado, Boulder. His main research interest is in the area of turbulence and transition simulation, a subject for which he has published numerous journal and conference articles. He obtained his BSc and MSc in mechanical engineering from Robert College, Istanbul, and earned his PhD in applied mechanics from the Université libre de Bruxelles. He is the principal editor of the book Industrial and Environmental Applications of Direct and Large Eddy Simulation and is an Associate Fellow of AIAA.

Dr. CHUEN-YEN CHOW is an Emeritus Professor of Aerospace Engineering at the University of Colorado, Boulder. After obtaining his PhD in aeronautical and astronautical Engineering from the University of Michigan in 1964, he taught at University of Notre Dame before joining University of Colorado in 1968. He is an Associate Fellow of AIAA, the coauthor of the third through fifth editions of the Foundations of Aerodynamics and author of An Introduction to Computational Fluid Mechanics (both from Wiley).

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