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Contents

1 Introduction
1.1 Scope of this book
1.2 Prediction Methods
1.1.1 Experimental Techniques
1.1.2 Analytical methods
1.1.3 CFD techniques
1.3 Typical problems
1.3.1 Aerospace applications
1.3.2 Automotive applications
1.3.3 Biomedical applications
1.4 Outline of this book
2. Basic Equations of Fluid Flow and Levels of Approximation
2.1 The Navier-Stokes Equations
2.1.1 Compressible fl ow
2.1.2 Incompressible fl ow
2.2 Turbulent fl ow
2.2.1 Turbulence modelling
2.3 Inviscid fl ow
2.4 Boundary layer approximation
2.5 Closure
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3. Basic Computational Techniques
3.1 Discretisation
3.1.1 Converting Derivatives to Discrete Expressions
3.1.2 Spatial Discretisation
3.2 Discretisation Methods
3.2.1 The Finite Difference Method
3.2.2 The Finite Element Method
3.2.3 The Finite Volume Method
3.2.4 Temporal Discretisation
3.3 The Accuracy of the Discretisation Process
3.4 Illustrative Example
3.5 Closure
4 Properties of Numerical Schemes
5 The Finite Difference Method
5.1 Basics
5.2 Other difference formulae
5.3 Multi-dimensional Finite difference formulae
5.4 Non-Uniform meshes
6 The Finite Element Method
6.1 Basics
6.2 Elements and Shape Functions
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Computational Fluid Dynamics Contents
6.2.1 One-dimensional elements
6.3 Weighted Residual Method
7 The Finite Volume Method
7.1 The diffusion equation
7.2 The Convection Diffusion Equation
7.2.1 The Upwind Scheme
7.3 Extension to multi-dimensional problems
7.4 Unstructured grids
8 Solution Methods Systems of Equations
8.1 Nonlinear Systems
8.1.1 Newton’s Method
8.1.2 Quasi-Newton Method
8.2 Methods for the solution of linear systems
8.3 Iterative methods
8.3.1 Basic iterative methods
8.4 Multigrid acceleration
9 Mesh Generation
9.1 Structured girds
9.1.1 Boundary-fi tted meshes
9.1.2 Algebraic grid generation
9.1.3 Partial Differential equation mesh generation
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9.2 Unstructured grids
9.2.1 Surface meshing
9.2.3 Delaunay triangulation
9.2.4 Other methods