 | Kühnlein Ch. Solution-adaptive moving mesh solver for geophysical flows: diss. / Deutsches Zentrum für Luft- und Raumfahrt, Institut Physik der Atmosphäre, Oberpfaffenhofen. - Köln: DLR, Bibliotheks- und Informationswesen, 2011. - ix, 159 p.: ill. - (Forschungsbericht; 2011-15). - Bibliogr.: p.145-159. - ISSN 1434-8454
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1 Introduction ................................................. 1
1.1 Adaptive moving mesh methods ............................ 5
1.2 Modelling framework and thesis approach ................ 10
1.3 Overview of the thesis ................................. 13
2 EULAG modelling framework ................................... 15
2.1 Analytical formulation ................................. 15
2.2 Numerical solution procedure ........................... 22
2.3 Advection solver MPDATA ................................ 25
3 MPDATA extension for time-dependent coordinates ............. 31
3.1 Compatible scalar transport ............................ 32
3.2 MPDATA compatibility ................................... 32
3.3 Discrete generalised anelastic mass conservation ....... 40
3.3.1 Diagnostic approach for the GMCL ................ 42
3.3.2 Prognostic approach for the generalised GCL ..... 43
3.4 Scalar advection experiments with a prescribed moving
mesh ................................................... 45
4 Solution-adaptive moving mesh algorithm ..................... 53
4.1 Conceptual approach .................................... 54
4.2 Variational formulation ................................ 55
4.3 Moving mesh partial differential equations ............. 56
4.4 Solution-adaptive moving mesh NFT solver ............... 66
5 Two-dimensional solution-adaptive moving mesh test
simulations ................................................. 73
5.1 Scalar advection ....................................... 76
5.2 Nonlinear evolution of a rising thermal ................ 83
5.3 Compatibility of MPDATA with the GMCL .................. 91
5.4 Summary ................................................ 96
6 Solution-adaptive moving mesh simulations with EULAG ........ 99
6.1 Baroclinic wave life cycle experiments ................ 102
7 Summary and conclusions .................................... 127
Appendices .................................................... 135
A Definition of the baroclinic thermal field .............. 135
B On the significance of baroclinic vorticity production
in the evolution of wake vortices ....................... 137
Acronyms ...................................................... 143
Nomenclature .................................................. 145
Bibliography .................................................. 147
Acknowledgements .............................................. 161
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