Computational Methods for Fluid Dynamics

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.- 1.8 Mathematical Classification of Flows.- 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.- 2.5 Properties of Numerical Solution Methods.- 2.6 Discretization Approaches.- 3. Finite Difference Methods.- 3.1 Introduction.- 3.2 Basic Concept.- 3.3 Approximation of the First Derivative.- 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.- 3.11 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.- 4.5 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.- 5.3 Iterative Methods.- 5.4 Coupled Equations and Their Solution.- 5.5 Non-Linear Equations and their Solution.- 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.- 6.3 Application to the Generic Transport Equation.- 6.4 Examples.- 7. Solution of the Navier-Stokes Equations.- 7.1 Special Features of the Navier-Stokes Equations.- 7.2 Choice of Variable Arrangement on the Grid.- 7.3 Calculation of the Pressure.- 7.4 Other Methods.- 7.5 Solution Methods for the Navier-Stokes Equations.- 7.6 Note on Pressure and Incompressibility.- 7.7 Boundary Conditions for the Navier-Stokes Equations.- 7.8 Examples.- 8. Complex Geometries.- 8.1 The Choice of Grid.- 8.2 Grid Generation.- 8.3 The Choice of Velocity Components.- 8.4 The Choice of Variable Arrangement.- 8.5 Finite Difference Methods.- 8.6 Finite Volume Methods.- 8.7 Control-Volume-Based Finite Element Methods.- 8.8 Pressure-Correction Equation.- 8.9 Axi-Symmetric Problems.- 8.10 Implementation of Boundary Conditions.- 8.11 Examples.- 9. Turbulent Flows.- 9.1 Introduction.- 9.2 Direct Numerical Simulation (DNS).- 9.3 Large Eddy Simulation (LES).- 9.4 RANS Models.- 9.5 Reynolds Stress Models.- 9.6 Very Large Eddy Simulation.- 10. Compressible Flow.- 10.1 Introduction.- 10.2 Pressure-Correction Methods for Arbitrary Mach Number.- 10.3 Methods Designed for Compressible Flow.- 11. Efficiency and Accuracy Improvement.- 11.1 Error Analysis and Estimation.- 12. Special Topics.- 12.1 Introduction.- 12.2 Heat and Mass Transfer.- 12.3 Flows With Variable Fluid Properties.- 12.4 Moving Grids.- 12.5 Free-Surface Flows.- 12.6 Meteorological and Oceanographic Applications.- 12.7 Multiphase flows.- 12.8 Combustion.- A. Appendices.- A.l List of Computer Codes and How to Access Them.- A.2 List of Frequently Used Abbreviations.- References.