A Computational Differential Geometry Approach to Grid Generation

✍ Scribed by Vladimir D. Liseikin

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 307
• Series: Scientific Computation
• Edition: 2nd
• Category: Library

✦ Synopsis

The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. In an updated and expanded Second Edition, this monograph gives a detailed treatment based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.

✦ Table of Contents

Preface to the Second Edition......Page 5
Contents......Page 11
1.1 Representation of Physical Geometries......Page 19
1.2 General Concepts Related to Grids......Page 22
1.3 Grid Generation Models......Page 30
1.4 Comprehensive Codes......Page 46
2.1 Jacobi Matrix......Page 49
2.2 Coordinate Lines, Tangential Vectors, and Grid Cells......Page 50
2.3 Coordinate Surfaces and Normal Vectors......Page 52
2.4 Representation of Vectors Through the Base Vectors......Page 54
2.5 Metric Tensors......Page 56
2.6 Cross Product......Page 60
2.7 Relations Concerning Second Derivatives......Page 63
3.1 Curves in Multidimensional Space......Page 69
3.2 Curves in Three-Dimensional Space......Page 71
4.1 Tangent and Normal Vectors and Tangent Plane......Page 75
4.2 First Groundform......Page 77
4.3 Generalization to Riemannian Manifolds......Page 81
4.4 Tensors......Page 88
4.5 Basic Invariants......Page 95
4.6 Geometry of Hypersurfaces......Page 99
4.7 Relations to the Principal Curvatures of Two-Dimensional Surfaces......Page 120
5 Comprehensive Grid Models......Page 131
5.1 Formulation of Di.erential Grid Generators......Page 133
5.2 Variational Formulations......Page 145
5.3 Formulation of Monitor Metrics......Page 154
6.1 General Forms of Equations......Page 175
6.2 Equations for Classical Monitor Metrics......Page 182
6.3 Role of the Mean Curvature......Page 196
6.4 Practical Grid Equations......Page 221
7.1 Method of Fractional Steps......Page 233
7.2 Method of Minimization of Energy Functional......Page 250
7.3 Generation of Multi-Block Grids......Page 269
7.4 Application of Layer-Type Functions to Grid Codes......Page 281
References......Page 293
Index......Page 303