A Computational Differential Geometry Approach to Grid Generation (Scientific Computation) - Hardcover

Vladimir D. Liseikin

Hardcover

ISBN 10: 3540140085 ISBN 13: 9783540140085

Publisher: Springer, 2003

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. This monograph describes in detail the eminent role played by differential geometry in grid technology based on mapping. It demonstrates how the Beltrami operator helps to develop robust multidimensional grid generation codes, while supplying related numerical code. In particular, procedures for the construction of monitor metric tensors are given and their qualitative effect on the resulting mesh is analyzed. Reviewing concepts from Riemannian geometry, the book applies them to general grids with prescribed properties, and discusses the role of mean and of Gaussian curvature and other geometric characteristics for the Beltrami equations for grid generation. It addresses scientists and practitioners as well as graduate students from applied mathematics, physics, and engineering.

About this title

From the Back Cover

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 edition the author takes a more detailed and practice-oriented approach towards explaining how to implement the method by:

• Employing 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.
• Providing 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.

Edition details

• Publisher: Springer
• Publication date: 2003
• ISBN 10: 3540140085
• ISBN 13: 9783540140085
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 264