## Fundamentals of Grid GenerationFundamentals of Grid Generation is an outstanding text/reference designed to introduce students in applied mathematics, mechanical engineering, and aerospace engineering to structured grid generation. It provides excellent reference material for practitioners in industry, and it presents new concepts to researchers. Readers will learn what boundary-conforming grids are, how to generate them, and how to devise their own methods. The text is written in a clear, intuitive style that doesn't get bogged down in unnecessary abstractions. Topics covered include planar, surface, and 3-D grid generation; numerical techniques; solution adaptivity; the finite volume approach to discretization of hosted equations; concepts from elementary differential geometry; and the transformation of differential operators to general coordinate systems. The book also reviews the literature on algebraic, conformal, orthogonal, hyperbolic, parabolic, elliptic, biharmonic, and variational approaches to grid generation. This unique volume closes with the author's original methods of variational grid generation. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Application to Hosted Equations | 25 |

Grid Generation on the Line | 45 |

Vector Calculus and Differential | 65 |

Classical Planar Grid Genera tion | 89 |

Varia tional Planar Grid Genera tion | 116 |

Tensor Analysis | 143 |

Advanced Planar Variational | 159 |

Grid Generation in Three | 181 |

Variational Grid Generation on Curves | 195 |

237 | |

Appendix A Tensor Coefficients | 251 |

283 | |

### Common terms and phrases

algorithm Appendix approach boundary conditions boundary value problem calculus chain rule Chapter coefficients conformal mappings conservative form constant continuum contravariant convex coordinate curves coordinate lines coordinate system covariant projection covariant tangents curvature defined derivatives Dirichlet discrete divergence divx equa Euler-Lagrange equations example Exercise Figure formulas geometry given gradient grid-generation equations homogeneous hosted equation inhomogeneous inverse iteration Jacobian matrix Lagrange Multiplier Laplacian Length functional linear logical domain logical space logical-space weight metric identity metric tensor minimize Modified Liao Neumann boundary conditions nonconservative form nonlinear null space numerical obtain one-dimensional parameter partial differential equations physical domain physical region physical space physical-space weight planar grid plane relationship right-hand side satisfies scalar second-order Section Show smooth solution solve stencil symmetric tangent vectors THEOREM three dimensions three-dimensional tion transfinite interpolation transformation truncation error TTM equations variables variational grid variational principle vector calculus Warsi weight function Winslow zero

### Popular passages

Page 237 - International Conference on Numerical Grid Generation in Computational Fluid Dynamics and Related Fields.

Page 241 - Numerical Grid Generation In Computational Fluid Mechanics 88, S. Sengupta, J. Hauser, PR Eiseman, and JF Thompson, eds., Pineridge Press, Swansea, UK, pp. 665-674 (also, NASA TM-101298). Baumeister, KJ and Horowitz, SJ, 1984, "Finite Element-Integral Acoustic Simulation of ]T15D Turbofan Engine," Journal of Vibration, Acoustics, Stress and Reliability in Design, Vol.

Page 242 - A numerical technique for two-dimensional grid generation with grid control at all of the boundaries", J.

Page 242 - A variational method for the optimization and adaption of grids in computational fluid dynamics. In Numerical Grid Generation in Computational Fluid Mechanics '88, S. Sengupta, J.

Page 238 - ... Math. Comp. 46, 1986, pp. 401-424. 5. JT Beale and A. Majda, High Order Accurate Vortex Methods with Explicit Velocity Kernels, J. Comp. Phys. 58, 1985, pp. 188-208. 6. JT Beale and A. Majda, Vortex Methods II: High Order Accuracy in 2 and 3 Dimensions, Math. Comp. 32, 1982, pp. 29-52. 7. JU Brackbill, Coordinate System Control: Adaptive Meshes, in Numerical Grid Generation, JF Thompson, ed., Elsevier, 1982. 8. AJ Chorin, A Numerical Study of Slightly Viscous Flow, J. Fluid Mech. 57, 1973, pp....

Page 237 - Anderson, DA 1986. Constructing adaptive grids with Poisson grid generators. In Numerical Grid Generation in Computational Fluid Dynamics, J. Haiiser and C. Taylor, eds., pp.

Page 246 - Roache, PJ and Steinberg, S., A new approach to grid generation using a variational formulation, AIAA 7th Computational Fluid Dynamics Conference, AIAA paper 85-1527, pp.