Basic Structured Grid Generation: With an introduction to unstructured grid generation

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Butterworth-Heinemann, Feb 11, 2003 - Mathematics - 256 pages
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Finite element, finite volume and finite difference methods use grids to solve the numerous differential equations that arise in the modelling of physical systems in engineering. Structured grid generation forms an integral part of the solution of these procedures. Basic Structured Grid Generation provides the necessary mathematical foundation required for the successful generation of boundary-conforming grids and will be an important resource for postgraduate and practising engineers.

The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids. The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front techniques.
  • A practical, straightforward approach to this complex subject for engineers and students.
  • A key technique for modelling physical systems.
 

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Contents

2 Classical differential geometry of space curves
30
3 Differential geometry of surfaces in E3
42
4 Structured grid generation algebraic methods
76
5 Differential models for grid generation
116
6 Variational methods and adaptive grid generation
152
7 Moving grids and timedependent co ordinate systems
180
8 Unstructured grid generation
190
Bibliography
227
Index
229
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Page 5 - P. of values. (In expressions involving general curvilinear co-ordinates the summation convention applies only when one of the repeated indices appears as a subscript and the other as a superscript.) The comparison shows that dx', dx'.
Page 3 - The position vector r of a point P in space with respect to...
Page 1 - Our objective in this book is to give an introduction to the most important aspects of grid generation.
Page 3 - O may be expressed as (1-1) where (ii , \2, 13}, alternatively written as {i, j, k), are unit vectors in the direction of the rectangular cartesian axes. We assume that there is an invertible relationship between this background set of cartesian co-ordinates and the set of curvilinear co-ordinates, ie with the inverse relationship x

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