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 |  موضوع: كتاب Basic Structured Grid Generation الأربعاء 13 أغسطس 2014, 1:21 am | |
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أخوانى فى الله
أحضرت لكم كتاب
Basic Structured Grid Generation
with an introduction to unstructured grid generation
M. Farrashkhalvat and J.P. Miles
ويتناول الموضوعات الأتية :
Contents
Preface ix
1. Mathematical preliminaries – vector and tensor analysis 1
1.1 Introduction 1
1.2 Curvilinear co-ordinate systems and base vectors in E3 1
1.3 Metric tensors 4
1.4 Line, area, and volume elements 8
1.5 Generalized vectors and tensors 8
1.6 Christoffel symbols and covariant differentiation 14
1.7 Div, grad, and curl 19
1.8 Summary of formulas in two dimensions 23
1.9 The Riemann-Christoffel tensor 26
1.10 Orthogonal curvilinear co-ordinates 27
1.11 Tangential and normal derivatives – an introduction 28
2. Classical differential geometry of space-curves 30
2.1 Vector approach 30
2.2 The Serret-Frenet equations 32
2.3 Generalized co-ordinate approach 35
2.4 Metric tensor of a space-curve 38
3. Differential geometry of surfaces in E3 42
3.1 Equations of surfaces 42
3.2 Intrinsic geometry of surfaces 46
3.3 Surface covariant differentiation 51
3.4 Geodesic curves 54
3.5 Surface Frenet equations and geodesic curvature 57
3.6 The second fundamental form 60
3.7 Principal curvatures and lines of curvature 63
3.8 Weingarten, Gauss, and Gauss-Codazzi equations 67
3.9 Div, grad, and the Beltrami operator on surfaces 70vi Contents
4. Structured grid generation – algebraic methods 76
4.1 Co-ordinate transformations 76
4.2 Unidirectional interpolation 80
4.2.1 Polynomial interpolation 80
4.2.2 Hermite interpolation polynomials 85
4.2.3 Cubic splines 87
4.3 Multidirectional interpolation and TFI 92
4.3.1 Projectors and bilinear mapping in two dimensions 92
4.3.2 Numerical implementation of TFI 94
4.3.3 Three-dimensional TFI 96
4.4 Stretching transformations 98
4.5 Two-boundary and multisurface methods 103
4.5.1 Two-boundary technique 103
4.5.2 Multisurface transformation 104
4.5.3 Numerical implementation 106
4.6 Website programs 108
4.6.1 Subdirectory: Book/univariate.gds 109
4.6.2 Subdirectory: Book/Algebra 109
4.6.3 Subdirectory: Book/bilinear.gds 112
4.6.4 Subdirectory: Book/tfi.gds 114
4.6.5 Subdirectory: Book/analytic.gds 115
5. Differential models for grid generation 116
5.1 The direct and inverse problems 116
5.2 Control functions 119
5.3 Univariate stretching functions 120
5.3.1 Orthogonality considerations 121
5.4 Conformal and quasi-conformal mapping 122
5.5 Numerical techniques 125
5.5.1 The Thomas Algorithm 125
5.5.2 Jacobi, Gauss-Seidel, SOR methods 127
5.5.3 The conjugate gradient method 129
5.6 Numerical solutions of Winslow equations 131
5.6.1 Thomas Algorithm 132
5.6.2 Orthogonality 134
5.7 One-dimensional grids 136
5.7.1 Grid control 136
5.7.2 Numerical aspects 139
5.8 Three-dimensional grid generation 140
5.9 Surface-grid generation model 141
5.10 Hyperbolic grid generation 142
5.11 Solving the hosted equations 143
5.11.1 An example 143
5.11.2 More general steady-state equation 145
5.12 Multiblock grid generation 146
5.13 Website programs 148
5.13.1 Subdirectory: Book/Winslow.gds 148Contents vii
5.13.2 Subdirectory: Book/one.d.gds 150
5.13.3 Subdirectory: Book/hyper.gds 150
5.13.4 Subdirectory: Book/p.d.Equations 151
6. Variational methods and adaptive grid generation 152
6.1 Introduction 152
6.2 Euler-Lagrange equations 153
6.3 One-dimensional grid generation 157
6.3.1 Variational approach 157
6.3.2 Dynamic adaptation 159
6.3.3 Space-curves 161
6.4 Two-dimensional grids 164
6.4.1 The L-functional and the Winslow model 165
6.4.2 The weighted L-functional 166
6.4.3 The weighted area-functional 167
6.4.4 Orthogonality-functional 167
6.4.5 Combination of functionals 168
6.4.6 Other orthogonality functionals 169
6.4.7 The Liao functionals 170
6.4.8 Surface grids 171
6.5 Harmonic maps 172
6.5.1 Surface grids 175
6.6 Website programs 177
6.6.1 Subdirectory: Book/var.gds 177
6.6.2 Subdirectory: Book/one.d.gds 179
7. Moving grids and time-dependent co-ordinate systems 180
7.1 Time-dependent co-ordinate transformations 180
7.2 Time-dependent base vectors 181
7.3 Transformation of generic convective terms 184
7.4 Transformation of continuity and momentum equations 185
7.4.1 Continuity equation 185
7.4.2 Momentum equations 185
7.5 Application to a moving boundary problem 187
8. Unstructured grid generation 190
8.1 Introduction 190
8.2 Delaunay triangulation 191
8.2.1 Basic geometric properties 191
8.2.2 The Bowyer-Watson algorithm 193
8.2.3 Point insertion strategies 196
8.3 Advancing front technique (AFT) 203
8.3.1 Introduction 203
8.3.2 Grid control 204
8.3.3 Searching algorithm 205
8.3.4 AFT algorithm 206viii Contents
8.3.5 Adaptation and parameter space 216
8.3.6 Grid quality improvement 216
8.4 Solving hosted equations using finite elements 217
8.5 Website programs 221
8.5.1 Subdirectory: book/Delaunay 221
Bibliography 227
Index
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