Page 240 - Basic Structured Grid Generation
P. 240
Index
Accepted and non-accepted triangles, 199 second-order tensors, 11
Adaptive methods, 153, 159–61, 216 surface base vectors, 48
ADI method, 134 surface vectors, 49
Advancing front technique (AFT), 203–15 Control functions, 119
Algebraic grid generation: Covariant:
interpolation, 80 base vectors, 2, 23
multisurface methods, 104 components of vectors, 8–9
transfinite interpolation (TFI), 92 second-order tensors, 11
two-boundary technique, 103 surface base vectors, 48
Alternating symbols, 13, 49 surface vectors, 49
Alternating surface tensor, 50 Covariant derivatives of:
Alternating tensor, 13 contravariant vectors, 18
Area element, 8, 49 covariant vectors, 18
Area co-ordinates of a point relative second-order and higher tensors, 19
to a triangle, 205 Curl:
Aspect ratio, 122 in rectangular cartesians, 21
in generalized form, 21–2
Background grid, 204 in two dimensions, 25
Beltrami operator, 74–5, 141 Curvilinear co-ordinate systems, 1–4
Bipolar co-ordinates, 114 bipolar co-ordinates, 115
Blending functions, 83 parabolic co-ordinates, 114–15
Boolean sum of transformations, 94, 98 spherical polar co-ordinates, 5, 44, 52
Bowyer–Watson algorithm, 193–6
Delaunay triangulation, 191–6
Chain rule, 3 Diagonal dominance, 126
Christoffel symbols: Diagonal swapping, 192, 217
for time-dependent problems, 182–3 Differential models for grid generation
of the first kind, 14–16 control functions, 119
of the second kind, 14–16 elliptic grid generators, 117
in orthogonal curvilinear co-ordinates, 27–8 hyperbolic grid generation, 142
transformation equations, 16 inverse problem, 117, 119
Circumcentre location, 223 one-dimensional grids, 136
Circumcircle property, 191 quasi-conformal mapping, 123
Computational space, 78, 80 surface grids, 141
Conformal mapping, 123 three-dimensional grids, 139
Conjugate gradient method, 129–1 TTM equations, 119
Connectivity table, 220 Winslow equations, 118
Continuity equation, 185 Directional derivatives of a scalar
Contravariant: normal to a co-ordinate surface, 29
base vectors, 3, 6–7, 24 tangential to a co-ordinate curve, 29
components of vectors, 8–9 Dirichlet tessellation, 191
