Adaptive Atmospheric Modeling (eBook)

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

Jörn Behrens (Autor)

eBook Download: PDF

2007 | 2006
XIX, 214 Seiten
Springer Berlin (Verlag)
978-3-540-33383-8 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 25.6.2007
• Reihe/Serie: Lecture Notes in Computational Science and Engineering
• Reihe/Serie: Lecture Notes in Computational Science and Engineering
• Zusatzinfo: XIX, 214 p. 74 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• Schlagworte: data structures • Geometry • Mathematica • Modeling • Simulation
• ISBN-10: 3-540-33383-5 / 3540333835
• ISBN-13: 978-3-540-33383-8 / 9783540333838