Holdings: Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model

Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model:

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Bibliographic Details
Main Author:	Ogaja, Jack (Author)
Format:	Thesis Book
Language:	English
Published:	Göttingen Cuvillier Verlag 2016
Subjects:	Eulersche Bewegungsgleichungen Klima Simulation Hochschulschrift
Online Access:	Inhaltsverzeichnis
Physical Description:	xvii, 133 Seiten Illustrationen, Diagramme
ISBN:	9783736992948

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adam_text	TABLE OF CONTENTS LIST OF T A B L E S..................................................................................................................XII LIST OF F IG U R E S ..............................................................................................................XIII LIST OF FREQUENTLY USED ABBREVIATIONS ........................................... ... . XVI NOTATION............................................................................................................................ XVII CHAPTER 1 INTRODUCTION ................................................................................... 1 1.1 O BJECTIVES............................................................................................................... 5 1.2 O UTLINE..................................................................................................................... 6 I FUNDAMENTALS, REVIEW AND THEORY 9 CHAPTER 2 HORIZONTAL DISCRETIZATION ON A STAGGERED GRID . . . 10 2.1 INTRODUCTION........................................................................................................... 10 2.2 NUMERICAL OPERATORS AND ERROR CONVERGENCE..........................................................12 2.2.1 INTERPOLATION OPERATORS ..............................................................................12 2.2.2 SPATIAL DIFFERENCING O PERATORS.....................................................................13 2.3 DISCRETIZATION OF NON-LINEAR TERMS ........................................................................14 2.3.1 QUASI-HIGHER ORDER ADVECTION SCHEMES ..................................................... 15 2.3.2 HIGHER ORDER ADVECTION S CH EM ES .............................................................. 17 2.3.3 QUADRATIC CONSERVING ADVECTION SCHEMES ............................................... 18 2.4 SUMMARY .................................................................................................................. 23 CHAPTER 3 ERRORS AND STABILITY ANALYSIS OF ADVECTION SCHEMES 25 3.1 INTRODUCTION ............................................................................................................ 25 3.2 ERROR ANALYSES ......................................................................................................... 27 3.2.1 DISCRETE DISPERSION RELATION, PHASE, AND PHASE SPEED APPROXI MATIONS ......................................................................................................... 27 3.2.2 GROUP VELOCITY APPROXIMATIONS .............................................................. 35 3.2.3 ALIAS ERROR ...................................................................................................36 3.3 LINEAR STABILITY ANALYSIS ..................................................................................... 40 3.4 EFFECTIVE RESOLUTION ANALYSIS ....................................................... 50 3.5 SUMMARY .................................................................................................................. 53 II THE M ODEL SYSTEM AND CODE IM PLEM ENTATION 61 CHAPTER 4 SPATIAL SCHEMES IN A NON-HYDROSTATIC M O D E L ............ 62 4.1 INTRODUCTION............................................................................................................... 62 4.2 THE MODEL S Y S TE M ................................................................................................... 62 4.3 COMPRESSIBLE EULER EQUATIONS IN TERRAIN-FOLLOWING COORDINATES ......................... 63 4.4 BOUNDARY C ONDITIONS................................................................................................ 64 4.5 QUASI-HIGHER ORDER ADVECTION SCHEMES ................................................................. 65 4.6 FOURTH ORDER ADVECTION SCHEME..............................................................................67 4.7 FOURTH ORDER QUADRATIC CONSERVING ADVECTION S CH EM E......................................67 4.8 FOURTH ORDER DISCRETIZATION OF FAST-WAVES TERM S.................................................. 68 4.9 NUMERICAL SCHEMES CONFIGURATIONS ........................................................................70 4.10 SUMMARY .................................................................................................................. 70 III CODE VERIFICATION AND REAL CASE STUDY 73 CHAPTER 5 IDEALIZED NUMERICAL T E S T S ....................................................... 74 5.1 INTRODUCTION............................................................................................................... 74 5.2 EULER EQUATIONS IN CARTESIAN COORDINATES ........................................................... 75 5.3 LINEAR ANALYTIC S O LU TIO N ..........................................................................................76 5.4 THE MODEL CONFIGURATION.......................................................................................... 78 5.5 ERROR N ORM S............................................................................................................... 79 5.6 TESTS Q U A LITY ............................................................................................................ 80 5.7 2D HYDROSTATIC LINEAR MOUNTAIN FLOW C A S E ........................................................ 81 5.8 2D NON-HYDROSTATIC LINEAR MOUNTAIN C A S E ........................................................... 82 5.9 VERTICAL FLUX OF HORIZONTAL M OM ENTUM ................................................................. 84 5.10 2D ATMOSPHERE AT REST TEST C A SE ...........................................................................88 5.10.1 NUMERICAL STABILITY T E S T ..............................................................................89 5.10.2 CONVERGENCE S TU D Y .......................................................................................90 5.11 SUMMARY .................................................................................................................. 91 CHAPTER 6 REAL CASE STUDY................................................................................94 6.1 C ONFIGURATION............................................................................................................ 95 6.2 SIMULATION STABILITY................................................................................................... 96 6.3 ZONAL SPECTRAL ANALYSIS.............................................................................................97 6.3.1 KINETIC ENERGY S PECTRA.................................................................................98 6.3.2 MODELS EFFECTIVE R ESOLUTION...................................................................... 101 6.3.3 PRECIPITATION S P ECTRA..................................................................................103 6.4 C LIM ATOLOGIES.......................................................................................................... 104 6.5 SUMMARY .................................................................................................................109 IV SUMMARY AND O UTLOOK 113 CHAPTER 7 SUMMARY AND OUTLOOK................................................................114 7.1 SUMMARY .................................................................................................................114 7.2 O U TLO O K ....................................................................................................................117 7.2.1 PHYSICS-DYNAMICS C O U P LIN G ......................................................................117 7.2.2 MODEL EFFICIENCY ........................................................................................ 118 V APPENDICES AND BIBLIOGRAPHY 119 APPENDIX A FINITE DIFFERENCE APPROXIM ATIONS .................................... 120 APPENDIX B NUMERICAL PROPERTIES OF THE MODEL*S SCHEMES . . . 122 B.L DISSIPATION PROPERTY OF UPWIND DIFFERENCE SCHEM ES .......................................... 122 B.2 CONSERVATIVE PROPERTY OF QUADRATIC CONSERVING S CH EM ES ................................. 123 APPENDIX C SUPPLEMENTARY F IG U R E S .............................................................127 REFERENCES.......................................................................................................................129
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spelling	Ogaja, Jack Verfasser aut Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model vorgelegt von B. Sc. Jack Ogaja Göttingen Cuvillier Verlag 2016 xvii, 133 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Dissertation Brandenburgische Technische Universität Cottbus-Senftenberg 2016 Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd rswk-swf Klima (DE-588)4031170-3 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Klima (DE-588)4031170-3 s Simulation (DE-588)4055072-2 s Eulersche Bewegungsgleichungen (DE-588)4219070-8 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029205910&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Ogaja, Jack Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd Klima (DE-588)4031170-3 gnd Simulation (DE-588)4055072-2 gnd
subject_GND	(DE-588)4219070-8 (DE-588)4031170-3 (DE-588)4055072-2 (DE-588)4113937-9
title	Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model
title_auth	Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model
title_exact_search	Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model
title_full	Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model vorgelegt von B. Sc. Jack Ogaja
title_fullStr	Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model vorgelegt von B. Sc. Jack Ogaja
title_full_unstemmed	Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model vorgelegt von B. Sc. Jack Ogaja
title_short	Higher Order Horizontal Discretization of Euler-Equations in a Non-Hydrostatic NWP and RCM Model
title_sort	higher order horizontal discretization of euler equations in a non hydrostatic nwp and rcm model
topic	Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd Klima (DE-588)4031170-3 gnd Simulation (DE-588)4055072-2 gnd
topic_facet	Eulersche Bewegungsgleichungen Klima Simulation Hochschulschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029205910&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT ogajajack higherorderhorizontaldiscretizationofeulerequationsinanonhydrostaticnwpandrcmmodel

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