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Adaptive Atmospheric Modeling Key Techniques in Grid Generation, Data Structures, and Numerical Operations with Applications

:	Jörn Behrens
:	Adaptive Atmospheric Modeling Key Techniques in Grid Generation, Data Structures, and Numerical Operations with Applications
:	Springer-Verlag
:	9783540333838
:	1
:	CHF 41.30
:

:	Allgemeines, Lexika
:	English

:	214
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This is an overview of the development of adaptive techniques for atmospheric modeling. Written in an educational style, it functions as a starting point for readers interested in adaptive modeling, in atmospheric sciences and beyond. Coverage includes paradigms of adaptive techniques, such as error estimation and adaptation criteria. Mesh generation methods are presented for triangular/tetrahedral and quadrilateral/hexahedral meshes, with a special section on initial meshes for the sphere.

	Preface	6
	Acknowledgements	7
	Contents	9
	List of Figures	12
	List of Tables	15
	1 Introduction	16
	1.1 Why Adaptivity?	17
	1.2 Who s Who in Adaptive Atmospheric Modeling	20
	1.3 Structure of the Text	21
	2 Principles of Adaptive Atmospheric Modeling	23
	2.1 Paradigms of Grid Refinement Resolution Enhancement Versus Error Equilibration	23
	2.2 Principle Difficulties with Adaptivity	24
	2.3 Abstract Adaptive Algorithm	26
	2.4 Dynamic Grid Adaptation h-Refinement	28
	2.5 Adapting the Order of Local Basis Functions p- Refinement	31
	2.6 Refinement Criteria	33
	3 Grid Generation	37
	3.1 Notation	37
	3.2 Grid Types	40
	3.3 Refinement Strategies in 2D	41
	3.4 Refinement in 3D	52
	3.5 Spherical Geometries	55
	4 Data Structures for Computational Efficiency	63
	4.1 Data Structures for Grid Management	63
	4.2 Data Structures for Efficient Numerical Calculations	68
	4.3 Working With Grid Patches	73
	4.4 Software Packages for Adaptive Grid Management	74
	4.5 Example for a Grid Handling Software Package amatos	75
	5 Issues in Parallelization of Irregularly Structured Problems	84
	5.1 Partitioning Strategies	85
	6 Numerical Treatment of Differential Operators on Adaptive Grids	92
	6.1 Approximating the Gradient	92
	6.2 Evaluating the Gradient Approximation	100
	7 Discretization of Conservation Laws	104
	7.1 Conservation Laws of Interest	105
	7.2 Finite Volume Methods	113
	7.3 Discontinuous Galerkin Methods	119
	7.4 Conservative Semi-Lagrangian Methods	123
	8 Example Applications	135
	8.1 Tracer Advection	135
	8.2 Inverse Tracer Advection	141
	8.3 Shallow Water Equations	144
	8.4 Wave Dispersion	150
	8.5 Test Cases	155
	9 Conclusions	164
	9.1 Evaluation of Methods	164
	9.2 Road Map for the Next Five Years	166
	A Some Basic Mathematical Tools	171
	B Metrics for Parallelizing Irregularly Structured Problems	173
	C Rotating Shallow Water Equations in Spherical Geometries	176
	D List of Notations	182
	References	184
	Index	209