Basic Structured Grid Generation - With an introduction to unstructured grid generation

Contents

Preface

1. Mathematical preliminaries – vector and tensor analysis

1.1 Introduction

1.2 Curvilinear co-ordinate systems and base vectors in E3

1.3 Metric tensors

1.4 Line, area, and volume elements

1.5 Generalized vectors and tensors

1.6 Christoffel symbols and covariant differentiation

1.7 Div, grad, and curl

1.8 Summary of formulas in two dimensions

1.9 The Riemann-Christoffel tensor

1.10 Orthogonal curvilinear co-ordinates

1.11 Tangential and normal derivatives – an introduction

2. Classical differential geometry of space- curves

2.1 Vector approach

2.2 The Serret-Frenet equations

2.3 Generalized co-ordinate approach

2.4 Metric tensor of a space-curve

3. Differential geometry of surfaces in E3

3.1 Equations of surfaces

3.2 Intrinsic geometry of surfaces

3.3 Surface covariant differentiation

3.4 Geodesic curves

3.5 Surface Frenet equations and geodesic curvature

3.6 The second fundamental form

3.7 Principal curvatures and lines of curvature

3.8 Weingarten, Gauss, and Gauss-Codazi equations

3.9 Div, grad, and the Beltrami operator on surfaces

4. Structured grid generation – algebraic methods

4.1 Co-ordinate transformations

4.2 Unidirectional interpolation

4.3 Multidirectional interpolation and TFI

4.4 Stretching transformations

4.5 Two-boundary and multisurface methods

4.6 Website programs

5. Differential models for grid generation

5.1 The direct and inverse problems

5.2 Control functions

5.3 Univariate stretching functions

5.4 Conformal and quasi-conformal mapping

5.5 Numerical techniques

5.6 Numerical solutions of Winslow equations

5.7 One-dimensional grids

5.8 Three-dimensional grid generation

5.9 Surface-grid generation model

5.10 Hyperbolic grid generation

5.11 Solving the hosted equations

5.12 Multiblock grid generation

5.13 Website programs

6. Variational methods and adaptive grid generation

6.1 Introduction

6.2 Euler-Lagrange equations

6.3 One-dimensional grid generation

6.4 Two-dimensional grids

6.5 Harmonic maps

6.6 Website programs

7. Moving grids and time-dependent co- ordinate systems

7.1 Time-dependent co-ordinate transformations

7.2 Time-dependent base vectors

7.3 Transformation of generic convective terms

7.4 Transformation of continuity and momentum equations

7.5 Application to a moving boundary problem

8. Unstructured grid generation

8.1 Introduction

8.2 Delaunay triangulation

8.3 Advancing front technique (AFT)

8.4 Solving hosted equations using finite elements

8.5 Website programs

Bibliography

Index