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
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