You are previewing Introduction to Computational Fluid Dynamics.
O'Reilly logo
Introduction to Computational Fluid Dynamics

Book Description

Introduction to Computational Fluid Dynamics is a self-contained introduction to a new subject, arising through the amalgamation of classical fluid dynamics and numerical analysis supported by powerful computers. Written in the style of a text book for advanced level B.Tech, M.Tech and M.Sc. students of various science and engineering disciplines. It introduces the reader to finite-difference and finite-volume methods for studying and analyzing linear and non-linear problems of fluid flow governed by inviscid incompressible and compressible Euler equations as also incompressible and compressible viscous flows governed by boundary-layer and Navier-Stokes equations. Simple turbulence modelling has been presented.

Table of Contents

  1. Cover
  2. Title page
  3. Contents
  4. About the Authors
  5. Dedication
  6. Preface
  7. Part I Finite Difference Method for Partial Differential Equations
    1. Chapter 1. Introduction and Mathematical Preliminaries
      1. 1.1 Introduction
      2. 1.2 Typical Partial Differential Equations in Fluid Dynamics
      3. 1.3 Types of Second-order Equations
      4. 1.4 Well-posed Problems
      5. 1.5 Properties of Linear and Quasilinear Equations
      6. 1.6 Physical Character of Subsonic and Supersonic Flows
      7. 1.7 Second-order Wave Equations
      8. 1.8 System of First-order Equations
      9. 1.9 Weak Solutions
      10. 1.10 Summary
      11. 1.11 Key Terms
    2. Chapter 2. Finite Difference and Finite Volume Discretisations
      1. 2.1 Introduction
      2. 2.2 Finite Difference Discretisation
      3. 2.3 Discretisation of Derivatives
      4. 2.4 Consistency, Convergence, and Stability
      5. 2.5 Finite Volume Discretisation
      6. 2.6 Face Area and Cell Volume
      7. 2.7 Summary
      8. 2.8 Key Terms
      9. 2.9 Exercise 2
    3. Chapter 3. Equations of Parabolic Type
      1. 3.1 Introduction
      2. 3.2 Finite Difference Scheme for Heat Conduction Equation
      3. 3.3 Crank-Nicholson Implicit Scheme
      4. 3.4 Analogy with Schemes for Ordinary Differential Equations
      5. 3.5 A Note on Implicit Methods
      6. 3.6 Leap-frog and DuFort–Frankel Schemes
      7. 3.7 Operator Notation
      8. 3.8 The Alternating Direction Implicit (ADI) Method
      9. 3.9 Summary
      10. 3.10 Key Terms
      11. 3.11 Exercise 3
    4. Chapter 4. Equations of Hyperbolic Type
      1. 4.1 Introduction
      2. 4.2 Explicit Schemes
      3. 4.3 Lax-Wendroff Scheme and Variants
      4. 4.4 Implicit Schemes
      5. 4.5 More on Upwind Schemes
      6. 4.6 Scalar Conservation Law: Lax-Wendroff and Related Schemes
      7. 4.7 Hyperbolic System of Conservation Laws
      8. 4.8 Second-order Wave Equation
      9. 4.9 Method of Characteristics for Second-order Hyperbolic Equations
      10. 4.10 Model Convection–Diffusion Equation
      11. 4.11 Summary
      12. 4.12 Key Terms
      13. 4.13 Exercise 4
    5. Chapter 5. Equations of Elliptić Type
      1. 5.1 Introduction
      2. 5.2 The Laplace Equation in Two Dimension
      3. 5.3 Iterative Methods for Solution of Linear Algebraic Systems
      4. 5.4 Solution of the Pentadiagonal System
      5. 5.5 Approximate Factorisation Schemes
      6. 5.6 Grid Generation Example
      7. 5.7 Body-fitted Grid Generation Using Elliptic-type Equations
      8. 5.8 Some Observations of AF Schemes
      9. 5.9 Multi-grid Method
      10. 5.10 Summary
      11. 5.11 Key Terms
      12. 5.12 Exercise 5
    6. Chapter 6. Equations of Mixed Elliptic–Hyperbolic Type
      1. 6.1 Introduction
      2. 6.2 Tricomi Equation
      3. 6.3 Transonic Computations Based on TSP Model
      4. 6.4 Summary
      5. 6.5 Key Terms
      6. 6.6 Exercise 6
  8. Part II Computational Fluid Dynamics
    1. Chapter 7. The Basic Equations of Fluid Dynamics
      1. 7.1 Introduction
      2. 7.2 Basic Conservation Principles
      3. 7.3 Unsteady Navier–Stokes Equations in Integral Form
      4. 7.4 Navier–Stokes Equations in Differential Form
      5. 7.5 Boundary Conditions for Navier–Stokes Equations
      6. 7.6 Reynolds Averaged Navier–Stokes Equations
      7. 7.7 Boundary-layer, Thin-layer and Associated Approximations
      8. 7.8 Euler Equations for Inviscid Flows
      9. 7.9 Boundary Conditions for Euler Equations
      10. 7.10 The Full Potential Equation
      11. 7.11 Inviscid Incompressible Irrotational Flow
      12. 7.12 Summary
      13. 7.13 Key Terms
    2. Chapter 8. Grid Generation
      1. 8.1 Introduction
      2. 8.2 Co-ordinate Transformation
      3. 8.3 Differential Equation Methods
      4. 8.4 Algebraic Methods
      5. 8.5 Transfinite Interpolation Methods
      6. 8.6 Unstructured Grid Generation
      7. 8.7 Mesh Adaptation
      8. 8.8 Summary
      9. 8.9 Key Terms
      10. 8.10 Exercise 8
    3. Chapter 9. Inviscid Incompressible Flow
      1. 9.1 Introduction
      2. 9.2 Potential Flow Problem
      3. 9.3 Panel Methods
      4. 9.4 Panel Methods (Continued)
      5. 9.5 More on Panel Methods
      6. 9.6 Panel Methods for Subsonic and Supersonic Flows
      7. 9.7 Summary
      8. 9.8 Key Terms
      9. 9.9 Exercise 9
    4. Chapter 10. Inviscid Compressible Flow
      1. 10.1 Introduction
      2. 10.2 Small-perturbation Flow
      3. 10.3 Numerical Solution of the Full Potential Equation
      4. 10.4 Full Potential Solution in Generalised Coordinates
      5. 10.5 Observations on the Full Potential Model
      6. 10.6 Euler Model
      7. 10.7 Boundary Conditions
      8. 10.8 Computed Examples Based on the Euler Model
      9. 10.9 Supersonic Flow Field Computation
      10. 10.10 Summary
      11. 10.11 Key Terms
      12. 10.12 Exercise 10
    5. Chapter 11. Boundary Layer Flow
      1. 11.1 Introduction
      2. 11.2 The Boundary Layer: Physical Considerations
      3. 11.3 The Boundary Layer Equations
      4. 11.4 Computations of the Laminar Boundary Layer
      5. 11.5 Turbulent Boundary Layers
      6. 11.6 Summary
      7. 11.7 Key Terms
      8. 11.8 Exercise 11
    6. Chapter 12. Viscous Incompressible Flow
      1. 12.1 Introduction
      2. 12.2 Incompressible Flow Computation
      3. 12.3 Stream-function Vorticity Approach
      4. 12.4 Primitive Variables Approach
      5. 12.5 The MAC Method
      6. 12.6 Solution Scheme
      7. 12.7 Case Study: Separated Flow in a Constricted Channel
      8. 12.8 Turbulent Flow
      9. 12.9 Summary
      10. 12.10 Key Terms
      11. 12.11 Exercise 12
    7. Chapter 13. Viscous Compressible Flow
      1. 13.1 Introduction
      2. 13.2 Dynamic Similarity
      3. 13.3 RANS (Reynolds Averaged Compressible Navier-Stokes) Equations
      4. 13.4 Turbulence Modelling
      5. 13.5 Boundary Conditions
      6. 13.6 Basic Computational Methods for Compressible Flow
      7. 13.7 Finite Volume Computation in 2D
      8. 13.8 Solution Procedure
      9. 13.9 Computational Results
      10. 13.10 Summary
      11. 13.11 Key Terms
      12. 13.12 Exercise 13
  9. Appendix A: Glossary
    1. A.1 Glossary
  10. Appendix B: Ready-made Softwares for CFD
    1. B.1 Introduction
    2. B.2 Software Packages for CFD
  11. Appendix C: Programs in the ‘C’ Language
    1. C.1 Program 3.1:ADI.C
    2. C.2 Program 4.1:LXMC.C
    3. C.3 Program 5.1:SOR.C
    4. C.4 Program 5.2:AFI.C
    5. C.5 Program 5.3:MGC.C
    6. C.6 Program 6.1:TSP.C
  12. Appendix D: Answers and Hints to Solutions
    1. D.1 Chapter 2
    2. D.2 Chapter 3
    3. D.3 Chapter 4
    4. D.4 Chapter 5
    5. D.5 Chapter 6
    6. D.6 Chapter 10
    7. D.7 Chapter 12
  13. Bibliography
  14. Acknowledgements
  15. Copyright