Computational Methods for Fluid Dynamics (Paperback, 3, Revised)

1. Basic Concepts of Fluid Flow.- 1.1 Introduction.- 1.2 Conservation Principles.- 1.3 Mass Conservation.- 1.4 Momentum Conservation.- 1.5 Conservation of Scalar Quantities.- 1.6 Dimensionless Form of Equations.- 1.7 Simplified Mathematical Models.- 1.7.1 Incompressible Flow.- 1.7.2 Inviscid (Euler) Flow.- 1.7.3 Potential Flow.- 1.7.4 Creeping (Stokes) Flow.- 1.7.5 Boussinesq Approximation.- 1.7.6 Boundary Layer Approximation.- 1.7.7 Modeling of Complex Flow Phenomena.- 1.8 Mathematical Classification of Flows.- 1.8.1 Hyperbolic Flows.- 1.8.2 Parabolic Flows.- 1.8.3 Elliptic Flows.- 1.8.4 Mixed Flow Types.- 1.9 Plan of This Book.- 2. Introduction to Numerical Methods.- 2.1 Approaches to Fluid Dynamical Problems.- 2.2 What is CFD?.- 2.3 Possibilities and Limitations of Numerical Methods.- 2.4 Components of a Numerical Solution Method.- 2.4.1 Mathematical Model.- 2.4.2 Discretization Method.- 2.4.3 Coordinate and Basis Vector Systems.- 2.4.4 Numerical Grid.- 2.4.5 Finite Approximations.- 2.4.6 Solution Method.- 2.4.7 Convergence Criteria.- 2.5 Properties of Numerical Solution Methods.- 2.5.1 Consistency.- 2.5.2 Stability.- 2.5.3 Convergence.- 2.5.4 Conservation.- 2.5.5 Boundedness.- 2.5.6 Realizability.- 2.5.7 Accuracy.- 2.6 Discretization Approaches.- 2.6.1 Finite Difference Method.- 2.6.2 Finite Volume Method.- 2.6.3 Finite Element Method.- 3. Finite Difference Methods.- 3.1 Introduction.- 3.2 Basic Concept.- 3.3 Approximation of the First Derivative.- 3.3.1 Taylor Series Expansion.- 3.3.2 Polynomial Fitting.- 3.3.3 Compact Schemes.- 3.3.4 Non-Uniform Grids.- 3.4 Approximation of the Second Derivative.- 3.5 Approximation of Mixed Derivatives.- 3.6 Approximation of Other Terms.- 3.7 Implementation of Boundary Conditions.- 3.8 The Algebraic Equation System.- 3.9 Discretization Errors.- 3.10 An Introduction to Spectral Methods.- 3.10.1 Basic Concept.- 3.10.2 Another View of Discretization Error.- 3.11 Example.- 4. Finite Volume Methods.- 4.1 Introduction.- 4.2 Approximation of Surface Integrals.- 4.3 Approximation of Volume Integrals.- 4.4 Interpolation and Differentiation Practices.- 4.4.1 Upwind Interpolation (UDS).- 4.4.2 Linear Interpolation (CDS).- 4.4.3 Quadratic Upwind Interpolation (QUICK).- 4.4.4 Higher-Order Schemes.- 4.4.5 Other Schemes.- 4.5 Implementation of Boundary Conditions.- 4.6 The Algebraic Equation System.- 4.7 Examples.- 5. Solution of Linear Equation Systems.- 5.1 Introduction.- 5.2 Direct Methods.- 5.2.1 Gauss Elimination.- 5.2.2 LU Decomposition.- 5.2.3 Tridiagonal Systems.- 5.2.4 Cyclic Reduction.- 5.3 Iterative Methods.- 5.3.1 Basic Concept.- 5.3.2 Convergence.- 5.3.3 Some Basic Methods.- 5.3.4 Incomplete LU Decomposition: Stone's Method.- 5.3.5 ADI and Other Splitting Methods.- 5.3.6 Conjugate Gradient Methods.- 5.3.7 Biconjugate Gradients and CGSTAB.- 5.3.8 Multigrid Methods.- 5.3.9 Other Iterative Solvers.- 5.4 Coupled Equations and Their Solution.- 5.4.1 Simultaneous Solution.- 5.4.2 Sequential Solution.- 5.4.3 Under-Relaxation.- 5.5 Non-Linear Equations and their Solution.- 5.5.1 Newton-like Techniques.- 5.5.2 Other Techniques.- 5.6 Deferred-Correction Approaches.- 5.7 Convergence Criteria and Iteration Errors.- 5.8 Examples.- 6. Methods for Unsteady Problems.- 6.1 Introduction.- 6.2 Methods for Initial Value Problems in ODEs.- 6.2.1 Two-Level Methods.- 6.2.2 Predictor-Corrector and Multipoint Methods.- 6.2.3 Runge-Kutta Methods.- 6.2.4 Other Methods.- 6.3 Application to the Generic Transport Equation.- 6.3.1 Explicit Methods.- 6.3.2 Implicit Methods.- 6.3.3 Other Methods.- 6.4 Examples.- 7. Solution of the Navier-Stokes Equations.- 7.1 Special Features of the Navier-Stokes Equations.- 7.1.1 Discretization of Convective and Viscous Terms.- 7.1.2 Discretization of Pressure Terms and Body Forces.- 7.1.3 Conservation Properties.- 7.2 Choice of Variable Arrangement on the Grid.- 7.2.1 Colocated Arrangement.- 7.2.2 Staggered Arrangements.- 7.3 Calculation of the Pressure.- 7.3.1 The Pressure Equatio