A Computational Differential Geometry Approach to Grid Generation

Vladimir D. Liseikin3-540-34235-4, 978-3-540-34235-9

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. This monograph gives a detailed treatment of applications of geometric methods to advanced grid technology. It focuses on and describes a comprehensive approach 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. In this second editionВ the author takesВ a more detailed and practice-orientedВ approach towards explaining how to implement the methodВ by:

EmployingВ geometric and numerical analyses of monitor metrics as the basis for developing efficient tools for controlling grid properties.

Describing new grid generation codes based on finite differences for generating both structured and unstructured surface and domain grids.

ProvidingВ examples of applications of the codes to the generation of adaptive, field-aligned, and balanced grids, to the solutions of CFD and magnetized plasmas problems.

The book addresses both scientists and practitioners in applied mathematics and numerical solution of field problems.

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Table of contents :
A Computational Differential Geometry Approach to Grid Generation……Page 1
Preface to Second Edition……Page 5
Contents……Page 11
1 – Introductory Notions……Page 15
2 – General Coordinate Systems in Domains……Page 44
3 – Geometry of Curves……Page 64
4 – Multidimensional Geometry……Page 70
5 – Comprehensive Grid Models……Page 122
6 – Inverted Equations……Page 166
7 – Numerical Implementation of Grid Generators……Page 224
References……Page 283
Index……Page 293