Computational Fluid Dynamics

Contents

1 Introduction

• 1.1  Scope of this book
• 1.2  Prediction Methods
• 1.3  Typical problems
• 1.4  Outline of this book

2 Basic Equations of Fluid Flow and Levels of Approximation

• 2.1  The Navier-Stokes Equations
• 2.2  Turbulent flow
• 2.3  Inviscid flow
• 2.4  Boundary layer approximation
• 2.5  Closure

3 Basic Computational Techniques

• 3.1  Discretisation
• 3.2  Discretisation Methods
• 3.3  The Accuracy of the Discretisation Process
• 3.4  Illustrative Example
• 3.5  Closure

4 Properties of Numerical Schemes

• 4.1  Basic definitions
• 4.2  Consistency
• 4.3  Stability

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
• 6.3  Weighted Residual Method

7 The Finite Volume Method

• 7.1  The diffusion equation
• 7.2  The Convection Diffusion Equation
• 7.3  Extension to multi-dimensional problems
• 7.4  Unstructured grids

8 Solution Methods Systems of Equations

• 8.1  Nonlinear Systems
• 8.2  Methods for the solution of linear systems
• 8.3  Iterative methods
• 8.4  Multigrid acceleration

9 Mesh Generation

• 9.1  Structured girds
• 9.2  Unstructured grids

10 References