Page 241 - Basic Structured Grid Generation
P. 241
230 Index
Distribution of sources, 205 in orthogonal curvilinear co-ordinates, 28
Divergence: in two dimensions, 25
in generalized form, 20–21 Liao functional, 170
in rectangular cartesians, 20 Line element, 8, 47
in two dimensions, 25
of a second-order tensor, 23 Metric tensor:
surface form, 73
contravariant, 4–7, 9, 11, 24
contravariant surface metric tensor, 48
Equidistribution, 40, 159 covariant, 4–7, 9, 11, 23
Euler–Lagrange equations, 54, 153–6 covariant surface metric tensor, 46–7
in orthogonal curvilinear co-ordinates, 27
Finite-difference formulas, 76–7 of a space-curve, 39
Finite element methods, 217–21 Metrics, 109
Modified Liao functional, 170
Momentum equations, 185
Galerkin method, 218 Multiblock grid generation, 147–8
Gauss–Seidel method, 128 Multisurface methods, 104–8
Generalized tensors:
alternating tensor, 13–14
associated components, 12 Numerical techniques:
curvature tensor, 26 ADI method, 134
dyadic products, 12 conjugate gradient method, 129
Geodesic curvature, 57–9, 63 Gauss-Seidel method, 128
Geometric conservation law, 183 Jacobi method, 128
Gradient vector: LSOR method, 142
in generalized form, 4, 24 method of steepest descents, 129
in rectangular cartesians, 4 SOR method, 128
surface forms, 71–2 Thomas Algorithm, 125
Grid point velocity, 181
Grid smoothing, 217 Orthogonal curvilinear co-ordinate
systems, 27–8
Harmonic maps, 172–6 Orthogonality functional, 167–8
Hermite interpolation polynomials, 85 Orthogonality two functional, 169
Hyperbolic grid generation, 142–3 Orthogonality three functional, 170
Orthogonality of grids, 108, 121–2, 134–6
Over-relaxation, 128
Identity operator, 13
Index:
lowering, 9 Point-insertion strategies, 196
raising, 9 at triangle circumcentres, 196
Interpolation polynomials: Voronoi-segment method, 199
cubic splines, 87–92 Positive definite, 47, 129
Hermite polynomials, 85–7 Projectors, 92
Lagrange polynomials, 81–3
Intrinsic derivatives, 36, 52 Quasi-conformal mapping, 123–125
Jacobian, 2, 9–10, 45, 50, 80, 180 Relative tensors, 14, 50
Riemann–Christoffel tensor, 26–7, 53
Kronecker symbol (delta), 3, 13
SOR method, 128
L-functional, 165–166 Space-curves, 30–41
Lagrange basis polynomials, 81–3 binormal vector, 32
Lagrange vector identity, 7 controlling grid density, 40–1
Laplacian operator: curvature, 31–2
in cartesian co-ordinates, 16 curve identity, 39
in generalized co-ordinates, 22 fundamental theorem, 34