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A Computational Differential Geometry Approach to Grid Generation

:	Vladimir D. Liseikin
:	A Computational Differential Geometry Approach to Grid Generation
:	Springer-Verlag
:	9783540342366
:	2
:	CHF 155.60
:

:	Allgemeines, Lexika
:	English

:	294
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

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.

	Preface to the Second Edition	5
	Contents	11
	Geometric Background to Grid Technology	16
	1 Introductory Notions	19
	1.1 Representation of Physical Geometries	19
	1.2 General Concepts Related to Grids	22
	1.3 Grid Generation Models	30
	1.4 Comprehensive Codes	46
	2 General Coordinate Systems in Domains	49
	2.1 Jacobi Matrix	49
	2.2 Coordinate Lines, Tangential Vectors, and Grid Cells	50
	2.3 Coordinate Surfaces and Normal Vectors	52
	2.4 Representation of Vectors Through the Base Vectors	54
	2.5 Metric Tensors	56
	2.6 Cross Product	60
	2.7 Relations Concerning Second Derivatives	63
	3 Geometry of Curves	69
	3.1 Curves in Multidimensional Space	69
	3.2 Curves in Three-Dimensional Space	71
	4 Multidimensional Geometry	75
	4.1 Tangent and Normal Vectors and Tangent Plane	75
	4.2 First Groundform	77
	4.3 Generalization to Riemannian Manifolds	81
	4.4 Tensors	88
	4.5 Basic Invariants	95
	4.6 Geometry of Hypersurfaces	99
	4.7 Relations to the Principal Curvatures of Two- Dimensional Surfaces	120
	Algorithms and Applications of Advanced Grid Technology	128
	5 Comprehensive Grid Models	131
	5.1 Formulation of Differential Grid Generators	133
	5.2 Variational Formulations	145
	5.3 Formulation of Monitor Metrics	154
	6 Inverted Equations	175
	6.1 General Forms of Equations	175
	6.2 Equations for Classical Monitor Metrics	182
	6.3 Role of the Mean Curvature	196
	6.4 Practical Grid Equations	221
	7 Numerical Implementation of Grid Generators	233
	7.1 Method of Fractional Steps	233
	7.2 Method of Minimization of Energy Functional	250
	7.3 Generation of Multi-Block Grids	269
	7.4 Application of Layer-Type Functions to Grid Codes	281
	References	293
	Index	303