COMPUTATIONAL FLUID DYNAMICS The Basics with …

1 COMPUTATIONAL FLUID DYNAMICS The Basics with Applications McGraw-Hill Series in Mechanical Engineering Consulting Editors Jack P. Holman, Southern Methodist University John R. Lloyd, Michigan State University Anderson: COMPUTATIONAL FLUID DYNAMICS : The Basics with Applications Anderson: Modern Compressible Flow: With Historical Perspective Arora: Introduction to Optimum Design Bray and Stanley: Nondestructive Evaluation: A Tool for Design, Manufacturing, and Service Burton: Introduction to Dynamic Systems Analysis Culp: Principles of Energy Conversion Dally: Packaging of Electronic Systems: A Mechanical Engineering Approach Dieter: Engineering Design: A Materials and Processing Approach Driels: linear Control Systems Engineering Eckert and Drake: Analysis of Heat and Mass Transfer Edwards and McKee: Fundamentals of Mechanical Component Design Gebhart: Heat Conduction and Mass Diffusion Gibson: Pn"nciples of Composite Material Mechanics Hamrock: Fundamentals of FLUID Film Lubrication Heywood: Internal Combustion Engine Fundamentals Hinze: Turbulence Holman: Experimental Methods for Engineers Howell and Buckius.

2 Fundamentals of Engineering Thermodynamics Hutton: Applied Mechanical Vibrations Juvinall: Engineering Considerations of Stress, Strain, and Strength Kane and Levinson: DYNAMICS : Theory and Applications Kays and Crawford: Convective Heat and Mass Transfer Kelly: Fundamentals of Mechanical Vibrations Kimbrell: Kinematics Analysis and Synthesis Kreider and Rabi: Heating and Cooling of Buildings Martin: Kinematics and DYNAMICS of Machines Modest: Radiative Heat Transfer Norton: Design of Machinery Phelan: Fundamentals of Mechanical Design Raven: Automatic Control Engineering Reddy: An Introduction to the Finite Element Method Rosenberg and Karnopp: Introduction to Physical Systems DYNAMICS Schlichting: Boundary-Layer Theory Shames: Mechanics of Fluids Sherman: Viscous Flow Shigley: Kinematic Analysis of Mechanisms Sh!gley and Mischke: Mechanical Engineering Design Shigley and Dicker: Theory of Machines and '"e h . Stirn D 1n, C amsms er. es1gn with Microprocessors for Mechanical Engineers Stoecker and Jones: Refrigeration and Air Conditioning Ullman: The Mechanical Design Process Vanderplaats: N_umerical Optimization: Techniques for Engineering D.

3 With Applications esign, Wa~k: A~vanced Thermodynamics for Engineers White: Viscous FLUID Flow Zeid: CAD/CAM Theory and Practice McGraw-Hill Series in Aeronautical and Aerospace Engineering Consulting Editor John D. Anderson, Jr., University of Maryland Anderson: COMPUTATIONAL FLUID DYNAMICS : The Basics with A l" . Anderson: Fundamentals of Aerodynamics PP icattons Anderson: Hypersonic and High Temneratur,e Gas Dy . A d .. r nam1cs n erson. Introduction to Flight :nderson: Modern Compressible Flow: With Historical Perspective Urton: Introduction to Dynamic Sustems An l . D' Azzo .. J' a ys1s and Houp1s: Linear Control System Analysis and D . D?naldson: Analysis of Aircraft Structures: An Introduction es1gn Gibson: Principles of Composite Material Me h . Ka L"ki c amcs ne, I ns, and Levinson: Spacecraft DYNAMICS Katz and Plotkin: Low-Speed Aerodynamics From Nelson: Flight Stability and Automatic Con~/ Wing Theory to Panel Methods Peery and Azar: Aircraft Structures Rivello: Theory and Analysis o Fliuht Structu s hli h 'J o res c.

4 C ting: Boundary Layer Theory White: Viscous FLUID Flow Wiesel: Spaceflight DYNAMICS Also Available from McGraw-Hill Schaum's Outline Series in Mechanical Engineering Most outlines include basic theory, definitions and hundreds of example problems solved in step-by-step detail, and supplementary problems with answers. Related titles on the current list include: Acoustics Continuum Mechanics Engineering Economics Engineering Mechanics FLUID DYNAMICS FLUID Mechanics & Hydraulics Heat Transfer Lagrangian DYNAMICS Machine Design Mathematical Handbook of Formulas & Tables Mechanical Vibrations Operations Research Statics & Mechanics of Materials Strength of Materials Theoretical Mechanics Thermodynamics for Engineers Thermodynamics with Chemical Applications Schaum's Solved Problems Books Each title in this series is a complete and expert source of solved problems with solutions worked out in step-by-step detail. Related titles on the current list include: 3000 Solved Problems in Calculus 2500 Solved Problems in Differential Equations 2500 Solved Problems in FLUID Mechanics & Hydraulics 1000 Solved Problems in Heat Transfer 3000 Solved Problems in Linear Algebra 2000 Solved Problems in Mechanical Engineering Thermodynamics 2000 Solved Problems in Numerical Analysis 700 Solved Problems in Vector Mechanics for Engineers: DYNAMICS 800 Solved Problems in Vector Mechanics for Engineers: Statics Available at most college bookstores, or for a complete list of titles and prices, write to: Schaum Division McGraw-Hill, Inc.

5 1221 Avenue of the Americas New York, NY 10020 COMPUTATIONAL FLUID DYNAMICS The Basics with Applications John D. Anderson, Jr. Department of Aerospace Engineering University of Maryland McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto COMPUTATIONAL FLUID DYNAMICS The Basics with Applications International Editions 1995 Exclusive rights by McGraw-Hill Book Co. - Singapore for manufacture and export. This book cannot be re-exported from the country to which it is consigned by McGraw-Hill. Copyright 1995 by McGraw-Hill, Inc. All rights reserved. Except as permitted under the Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. 2 3 4 5 6 7 8 9 0 BJE FC 9 8 7 6 This book was set in Times Roman.

6 The editors were John J. Corrigan and Eleanor Castellano; the production supervisor was Denise L. Puryear. The cover was designed by Rafael Hernandez. Library of Congress Cataloging-in-Publication Data Anderson, John David. COMPUTATIONAL FLUID DYNAMICS : Basics with applications I John D. Anderson, Jr. p. cm. - (McGraw-Hill series in mechanical engineering-McGraw-Hill series in aeronautical and aerospace engineering) Includes bibliographical references and index. ISBN 0-07-001685-2 I. FLUID DYNAMICS -Data processing. I. Title. II. Series. QA9 II .A58 1995 532'.05'0 I 5 II 8-dc20 94-21237 When ordering this title, use ISBN 0-07-11321()-4 Printed in Singapore ABOUT THE AUTHOR John D. Anderson, Jr., was born in Lancaster, Pennsylvania, on October 1, 1937. He attended the University of Florida, graduating in 1959 with high honors and a Bachelor of Aeronautical Engineering Degree. From 1959 to 1962, he was a lieutenant and task scientist at the Aerospace Research Laboratory at Wright-Patterson Air Force Base.

7 From 1962 to 1966, he attended the Ohio State University under the National Science Foundation and NASA Fellowships, graduating with a in aeronautical and astronautical engineering. In 1966 he joined the Naval Ordnance Laboratory as Chief of the Hypersonic Group. In 1973, he became Chairman of the Department of Aerospace Engineering at the University of Maryland. and since 1980 has been professor of Aerospace Engineering at Maryland. In 1982, he was designated a Distinguished Scholar/Teacher by the University. During 1986-1987, while on sabbatical from the university, Dr. Anderson occupied the Charles Lindbergh chair at the National Air and Space Museum of the Smithsonian Institution. He continues with the Museum in a part-time appointment as special assistant for aerodynamics. In addition to his appoint-ment in aerospace engineering, in 1993 he was elected to the faculty of the Committee on the History and Philosophy of Science at Maryland. Dr. Anderson has published five books: Gasdynamic Lasers: An Introduction, Academic Press (1976), and with McGraw-Hill, Introduction to Flight, 3d edition (1989), Modern Compressible Flow, 2d Edition (1990), Fundamentals of Aerodynamics, 2d edition (1991 ), and Hypersonic and High Temperature Gas DYNAMICS ( 1989).

8 He is the author of over 100 papers on radiative gasdynamics, re-entry aerothermodynamics, gas dynamic and chemical lasers, COMPUTATIONAL FLUID DYNAMICS , applied aerodynamics, hypersonic flow, and the history of aerodynamics. Dr. Anderson is in Who s Who in America, and is a Fellow of the American Institute of Aeronautics and Astronautics (AIAA). He is also a Fellow of the Washington Academy of Sciences, and a member of Tau Beta Pi, Sigma Tau, Phi Kappa Phi, Phi Eta Sigma, The American Society for Engineering Education (ASEE), The Society for the History of Technology, and the History of Science Society. He has received the Lee Atwood Award for excellence in Aerospace Engineering Education from the AIAA and the ASEE. To SARAH-ALLEN, KATHERINE, AND ELIZABETH for all their love and understanding CONTENTS Preface xix Part I Basic Thoughts and Equations 1 Philosophy of COMPUTATIONAL FLUID DYNAMICS 3 COMPUTATIONAL FLUID DYNAMICS : Why? 4 COMPUTATIONAL FLUID DYNAMICS as a Research Tool 6 COMPUTATIONAL FLUID DYNAMICS as a Design Tool 9 The Impact of COMPUTATIONAL FLUID DYNAMICS -Some Other Examples 13 l Automobile and Engine Applications 14 Industrial Manufacturing Applications 17 Civil Engineering Applications 19 Environmental Engineering Applications 20 Naval Architecture Applications (Submarine Example) 22 COMPUTATIONAL FLUID DYNAMICS : What Is It?

9 23 The Purpose of This Book 32 2 The Governing Equations of FLUID DYNAMICS : Their Derivation, a Discussion of Their Physical Meaning, and a Presentation of Forms Particularly Suitable to CFD 37 Introduction 38 Models of the Flow 40 l Finite Control Volume 41 Infinitesimal FLUID Element 42 Some Comments 42 The Substantial Derivative (Time Rate of Change Following a Moving FLUID Element 43 The Divergence of the Velocity: Its Physical Meaning 47 A Comment 48 xi xii CONTENTS CONTENTS xiii The Continuity Equation 49 Difference Equations 142 Model of the Finite Control Volume Fixed in Space 49 Explicit and Implicit Approaches: Definitions and Contrasts 145 Model of the Finite Control Volume Moving with the Errors and an Analysis of Stability 153 FLUID 51 Stability Analysis: A Broader Perspective 165 Model of an Infinitesimally Small Element Fixed Summary 165 in Space 53 GUIDEPOST Model of an Infinitesimally Small FLUID Element 166 Moving with the Flow 55 Problems 167 All the Equations Are One: Some Manipulations 56 Integral versus Differential Form of the Equations: 5 Grids with Appropriate Transformations 168 An Important Comment 60 Introduction 168 The Momentum Equation 60 General Transformation of the Equations 66 171 The Energy Equation Metrics and Jacobians 178 Summary of the Governing Equations for FLUID DYNAMICS : Form of the Governing Equations Particularly Suited With Comments 75 for CFD Revisited: The Transformed Version 183 Equations for Viscous Flow (the Navier-Stokes A Comment 186 Equations) 75 Stretched (Compressed) Grids 186 Equations for Inviscid Flow (the Euler Equations) 77 Boundary-Fitted Coordinate Systems.)

10 Elliptic Grid Comments on the Governing Equations 78 Physical Boundary Conditions 80 Generation 192 O Forms of the Governing Equations Particularly Suited for GUIDEPOST 193 CFD: Comments on the Conservation Form, Shock Fitting, and Shock Capturing 82 Adaptive Grids 200 Summary 92 Some Modem Developments in Grid Generation 208 Problems 93 Some Modem Developments in Finite-Volume Mesh Generation: Unstructured Meshes and a Return to Cartesian 3 Mathematical Behavior of Partial Differential Meshes 210 Equations: The Impact on CFD 95 Summary 212 Introduction 95 Problems 215 Classification of Quasi-Linear Partial Differential Equations 97 A General Method of Determining the Classification of 6 Some Simple CFD Techniques: A Beginning 216 Partial Differential Equations: The Eigenvalue Method 102 Introduction 216 General Behavior of the Different Classes of Partial The Lax-Wendroff Technique 217 Differential Equations: Impact on Physical and MacCormack's Technique 222 COMPUTATIONAL FLUID DYNAMICS 105 Hyperbolic Equations 106 GUIDEPOST 223 Parabolic Equations 111 Some Comments: Viscous Flows, Conservation Form, Elliptic Equations 117 and Space Marching 225 Some Comments: The Supersonic Blunt Body Viscous Flows 225 Problem Revisited 119 Conservation Form 225 Well-Posed Problems 120 Space Marching 226 Summary 121 The Relaxation Technique and Its Use with Low-Speed Problems 121 Inviscid Flow 229 Aspects of Numerical Dissipation and Dispersion.