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Grid Generation Methods

:	Vladimir D. Liseikin
:	Grid Generation Methods
:	Springer-Verlag
:	9789048129126
:	2
:	CHF 107.00
:

:	Allgemeines, Lexika
:	English

:	390
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.

	Preface to the Second Edition	6
	Contents	12
	1 General Considerations	19
	Introduction	19
	General Concepts Related to Grids	20
	Grid Cells	21
	Requirements Imposed on Grids	23
	Grid Size and Cell Size	23
	Grid Organization	24
	Cell and Grid Deformation	24
	Consistency with Geometry	25
	Consistency with Solution	25
	Compatibility with Numerical Methods	27
	Grid Classes	28
	Structured Grids Generated by Mapping Approach	28
	Realization of Grid Requirements	29
	Coordinate Grids	30
	Boundary-Conforming Grids	31
	Shape of Computational Domains	32
	Unstructured Grids	33
	Block-Structured Grids	34
	Communication of Adjacent Coordinate Lines	35
	Topology of the Grid	35
	Conditions Imposed on Grids in Blocks	37
	Overset Grids	38
	Hybrid Grids	39
	Approaches to Grid Generation	39
	Methods for Structured Grids	40
	Algebraic Methods	40
	Differential Methods	40
	Variational Methods	41
	Methods for Unstructured Grids	41
	Octree Approach	41
	Delaunay Approach	42
	Advancing-Front Techniques	42
	Big Codes	43
	Interactive Systems	44
	New Techniques	45
	Domain Decomposition	45
	New Methods	45
	Comments	46
	2 Coordinate Transformations	48
	Introduction	48
	General Notions and Relations	49
	Jacobi Matrix	49
	Tangential Vectors	50
	Normal Vectors	52
	Representation of Vectors Through the Base Vectors	53
	Metric Tensors	55
	Covariant Metric Tensor	55
	Contravariant Metric Tensor	56
	Geometric Interpretation	56
	Relations Between Covariant and Contravariant Elements	57
	Cross Product	58
	Geometric Meaning	58
	Relation to Volumes	59
	Relation to Base Vectors	60
	Relations Concerning Second Derivatives	61
	Christoffel Symbols	61
	Differentiation of the Jacobian	63
	Basic Identity	64
	Conservation Laws	66
	Scalar Conservation Laws	66
	Mass Conservation Law	67
	Convection-Diffusion Equation	67
	Laplace Equation	68
	Vector Conservation Laws	68
	Example	70
	Time-Dependent Transformations	72
	Reformulation of Time-Dependent Transformations	72
	Basic Relations	73
	Velocity of Grid Movement	73
	Derivatives of the Jacobian	74
	Basic Identity	75
	Equations in the Form of Scalar Conservation Laws	75
	Examples of Scalar Conservation-Law Equations	76
	Parabolic Equation	76
	Mass Conservation Law	77
	Convection-Diffusion Equation	77
	Energy Conservation Law	77
	Linear Wave Equation	78
	Lagrangian Coordinates	79
	Equations in the Form of Vector Conservation Laws	79
	Comments	83
	3 Grid Quality Measures	84
	Introduction	84
	Curve Geometry	84
	Basic Curve Vectors	85
	Tangent Vector	85
	Curves in Three-Dimensional Space	86
	Curvature	87
	Torsion	88
	Surface Geometry	89
	Surface Base Vectors	89
	Metric Tensors	90
	Covariant Metric Tensor	90
	Contravariant Metric Tensor	91
	Second Fundamental Form	92
	Surface Curvatures	92
	Principal Curvatures	92
	Mean Curvature	93
	Gaussian Curvature	94
	Metric-Tensor Invariants	94
	Algebraic Expressions for the Invariants	95
	Geometric Interpretation	96
	Characteristics of Grid Lines	97
	Sum of Squares of Cell Edge Lengths	98
	Eccentricity	98
	Curvature	99
	Local Straightness of the Coordinate Line	99
	Expansion of the Curvature Vector in the Normal Vectors	100
	Measure of Coordinate Line Curvature	101
	Measure of Coordinate Line Torsion	102
	Characteristics of Faces of Three-Dimensional Grids	102
	Cell Face Skewness	102
	Face Aspect-Ratio	103
	Cell Face Area Squared	103
	Cell Face Warping	104
	Mean Curvature of the Coordinate Surface	104
	Gaussian Curvature of the Coordinate Surface	105
	Measures of Face Warping	105
	Characteristics of Grid Cells	105
	Cell Aspect-Ratio	106
	Square of Cell Volume	106
	Cell Area Squared	106
	Cell Skewness	106
	Characteristics of Nonorthogonality	107
	Grid Density	108
	Characteristics of Deviation from Conformality	109
	Two-Dimensional Space	110
	Evaluation of the Cell Angles	110
	Evaluation of the Cell Aspect Ratio	111
	Three-Dimensional Space	112
	Generalization to Arbitrary Dimensions	113
	Grid Eccentricity	113
	Measures of Grid Warping and Grid Torsion	113