Basic structured grid generation with an introduction to unstructured grid generation

M Farrashkhalvat, J P Miles9780750650588, 0-7506-5058-3

Finite element, finite volume and finite difference methods use grids to solve the numerous differential equations that arise in the modelling of physical systems in engineering. Structured grid generation forms an integral part of the solution of these procedures. Basic Structured Grid Generation provides the necessary mathematical foundation required for the successful generation of boundary-conforming grids and will be an important resource for postgraduate and practising engineers. The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids. The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front techniques. A companion website fully supports this book by providing numerical codes in FORTRAN 77/90 for both structured and unstructured grid generation which will help the reader to develop their understanding and make progress in grid generation. * A practical, straightforward approach to this complex subject for engineers and students. * A key technique for modelling physical systems. * Companion website provides free access to grid generation codes.

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Table of contents :
Contents……Page 6
Preface……Page 10
1.2 Curvilinear co-ordinate systems and base vectors in E3……Page 12
1.3 Metric tensors……Page 15
1.5 Generalized vectors and tensors……Page 19
1.6 Christoffel symbols and covariant differentiation……Page 25
1.7 Div, grad, and curl……Page 30
1.8 Summary of formulas in two dimensions……Page 34
1.9 The Riemann-Christoffel tensor……Page 37
1.10 Orthogonal curvilinear co-ordinates……Page 38
1.11 Tangential and normal derivatives – an introduction……Page 39
2.1 Vector approach……Page 41
2.2 The Serret-Frenet equations……Page 43
2.3 Generalized co-ordinate approach……Page 46
2.4 Metric tensor of a space-curve……Page 49
3.1 Equations of surfaces……Page 53
3.2 Intrinsic geometry of surfaces……Page 57
3.3 Surface covariant differentiation……Page 62
3.4 Geodesic curves……Page 65
3.5 Surface Frenet equations and geodesic curvature……Page 68
3.6 The second fundamental form……Page 71
3.7 Principal curvatures and lines of curvature……Page 74
3.8 Weingarten, Gauss, and Gauss-Codazi equations……Page 78
3.9 Div, grad, and the Beltrami operator on surfaces……Page 81
4.1 Co-ordinate transformations……Page 87
4.2 Unidirectional interpolation……Page 91
4.3 Multidirectional interpolation and TFI……Page 103
4.4 Stretching transformations……Page 109
4.5 Two-boundary and multisurface methods……Page 114
4.6 Website programs……Page 119
5.1 The direct and inverse problems……Page 127
5.2 Control functions……Page 130
5.3 Univariate stretching functions……Page 131
5.4 Conformal and quasi-conformal mapping……Page 133
5.5 Numerical techniques……Page 136
5.6 Numerical solutions of Winslow equations……Page 142
5.7 One-dimensional grids……Page 147
5.8 Three-dimensional grid generation……Page 151
5.9 Surface-grid generation model……Page 152
5.10 Hyperbolic grid generation……Page 153
5.11 Solving the hosted equations……Page 154
5.12 Multiblock grid generation……Page 157
5.13 Website programs……Page 159
6.1 Introduction……Page 163
6.2 Euler-Lagrange equations……Page 164
6.3 One-dimensional grid generation……Page 168
6.4 Two-dimensional grids……Page 175
6.5 Harmonic maps……Page 183
6.6 Website programs……Page 188
7.1 Time-dependent co-ordinate transformations……Page 191
7.2 Time-dependent base vectors……Page 192
7.3 Transformation of generic convective terms……Page 195
7.4 Transformation of continuity and momentum equations……Page 196
7.5 Application to a moving boundary problem……Page 198
8.1 Introduction……Page 201
8.2 Delaunay triangulation……Page 202
8.3 Advancing front technique (AFT)……Page 214
8.4 Solving hosted equations using finite elements……Page 228
8.5 Website programs……Page 232
Bibliography……Page 238
Index……Page 240