Page 8 - Introduction to Computational Fluid Dynamics

P1: JZP
CB908/Date
0521853265pre

Contents 0 521 85326 5 May 27, 2005 0:54

Nomenclature page xiii

Preface xvii

1. Introduction..........................................1
1.1 CFD Activity 1
1.2 Transport Equations 2
1.3 Numerical Versus Analytical Solutions 5
1.4 Main Task 6
1.5 A Note on Navier–Stokes Equations 9
1.6 Outline of the Book 12
Exercises 13

2. 1D Heat Conduction................................17

2.1 Introduction 17
2.2 1D Conduction Equation 17
2.3 Grid Layout 19
2.4 Discretisation 20
2.4.1 TSE Method 21
2.4.2 IOCV Method 23
2.5 Stability and Convergence 24
2.5.1 Explicit Procedure ψ = 0 25
2.5.2 Partially Implicit Procedure 0 <ψ < 1 28
2.5.3 Implicit Procedure ψ = 1 29
2.6 Making Choices 31
2.7 Dealing with Nonlinearities 32
2.7.1 Nonlinear Sources 33
2.7.2 Nonlinear Coefficients 33

vii