An Introduction to Computational Fluid Mechanics by Example

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 Universite 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).

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 Karman 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 Benard 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