Holdings: Simulation of low Mach number astrophysical flows

Simulation of low Mach number astrophysical flows:

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Bibliographic Details
Main Author:	Miczek, Fabian (Author)
Format:	Thesis Book
Language:	English
Published:	2013
Subjects:	Hochschulschrift
Online Access:	Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130508-1127720-0-4 Inhaltsverzeichnis
Physical Description:	156 S. graph. Darst.

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MARC


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adam_text	IMAGE 1 CONTENTS 1 INTRODUCTION: PRINCIPLES OF STELLAR EVOLUTION AND OPEN QUESTIONS 7 1.1 PHYSICAL PROCESSES IN STARS 7 1.2 STELLAR EVOLUTION MODELING 10 1.3 LIMITATIONS AND OPEN QUESTIONS 11 1.4 HYDRODYNAMIC TREATMENT OF STARS 12 1.5 GOALS AND ORGANIZATION OF THIS THESIS 14 2 GOVERNING EQUATIONS 16 2.1 EULER EQUATIONS 16 2.2 EQUATIONS OF STATE 17 2.2.1 GENERAL DESCRIPTION 17 2.2.2 IDEAL GAS 18 2.2.3 IDEAL GAS WITH RADIATION PRESSURE 19 2.3 GRAVITY 20 2.3.1 SOURCE TERMS 20 2.3.2 HYDROSTATIC EQUILIBRIUM 21 2.4 THERMAL RADIATION 21 2.5 NON-DIMENSIONALIZATION 22 2.6 LOW MACH NUMBER ASYMPTOTICS 23 2.6.1 SOUND WAVES 24 2.6.2 INCOMPRESSIBLE FLOW 24 2.6.3 GENERAL BEHAVIOR 25 2.6.4 KINETIC ENERGY 26 2.7 LOW MACH NUMBER APPROACHES 26 2.7.1 BOUSSINESQ APPROXIMATION 26 2.7.2 ANELASTIC EQUATIONS 28 2.7.3 FULLY COMPRESSIBLE APPROACH 28 3 BASIC DISCRETIZATION TECHNIQUES 29 3.1 GENERAL COORDINATE TRANSFORMATIONS 29 3.1.1 TRANSFORMATION OF THE EULER EQUATIONS 30 3.1.2 TRANSFORMATIONS FOR THERMAL RADIATION 31 3.2 FINITE VOLUME DISCRETIZATION 31 3.3 COMPUTATION OF THE GEOMETRIC TERMS 33 3.3.1 GENERAL STRATEGY 33 3.3.2 CONSISTENCY RELATIONS 34 3.3.3 CARTESIAN GEOMETRY 34 3.4 RECONSTRUCTION OF INTERFACE VALUES 35 3.4.1 GENERAL CONSIDERATIONS 35 3.4.2 CONSTANT RECONSTRUCTION 36 3.4.3 LINEAR RECONSTRUCTION 36 3.5 NUMERICAL FLUX FUNCTIONS 36 3.5.1 THE RIEMANN PROBLEM 36 3.5.2 ROE S APPROXIMATE RIEMANN SOLVER 37 3.5.3 OTHER FLUX FUNCTIONS 38 3 HTTP://D-NB.INFO/1038115728 IMAGE 2 3.5.4 THERMAL RADIATION 39 3.6 BOUNDARY CONDITIONS 40 3.6.1 GHOST CELLS 40 3.6.2 FLUX BOUNDARY CONDITIONS 41 4 NUMERICAL FLUX FUNCTIONS IN THE LOW MACH NUMBER REGIME 43 4.1 NUMERICAL VISCOSITY 43 4.1.1 GRESHO VORTEX 43 4.1.2 GODUNOV-LIKE SCHEMES 44 4.2 LOW MACH NUMBER SCALING 46 4.2.1 ARTIFICIAL SOUND WAVES 46 4.2.2 ANALYSIS OF NUMERICAL FLUX FUNCTIONS 47 4.3 LOW MACH NUMBER FLUXES 48 4.3.1 ROE-TURKEL SCHEME 48 4.3.2 ANALYSIS OF THE ROE-TURKEL SCHEME 50 4.3.3 A NEW LOW MACH NUMBER PRECONDITIONER 51 4.3.4 VFROE-LOWMACH SCHEME 52 4.3.5 AUSM + SCHEMES 52 4.3.6 LOW MACH NUMBER RECONSTRUCTION 54 4.4 VALIDATION AND COMPARISON 55 5 TEMPORAL DISCRETIZATION 58 5.1 EXPLICIT TIME STEPPING 58 5.2 IMPLICIT TIME STEPPING 59 5.2.1 THE BACKWARD EULER SCHEME 59 5.2.2 ESDIRK SCHEMES 61 5.3 TIME STEP DETERMINATION 62 5.3.1 CFL-LIKE CRITERIA 62 5.3.2 ESDIRK ERROR ESTIMATOR 63 5.4 NON-LINEAR EQUATIONS 64 5.4.1 GENERAL PROPERTIES AND THE TREATMENT OF SCALAR FIELDS 64 5.4.2 NEWTON-RAPHSON METHOD 66 5.4.3 COMPUTATION OF THE DEFECT JACOBIAN MATRIX 67 5.5 SOLVERS FOR THE LINEAR SYSTEMS 69 5.5.1 DIRECT SOLVERS 69 5.5.2 ITERATIVE SOLVERS 70 5.5.3 MATRIX PRECONDITIONING 71 5.6 VALIDATION 73 5.6.1 ACCURACY 73 5.6.2 EFFICIENCY 79 6 NEARLY HYDROSTATIC FLOWS 83 6.1 DISCRETIZATION OF GRAVITY 83 6.1.1 POINTWISE GRAVITY 83 6.1.2 F-WAVE RIEMANN SOLVER 86 6.1.3 HYDROSTATIC RECONSTRUCTION 88 6.2 STABILITY OF ID HYDROSTATIC ATMOSPHERES 89 6.3 STABILITY OF 2D HYDROSTATIC ATMOSPHERES 94 6.3.1 BASIC SETUP 94 6.3.2 HYDROSTATIC NUMERICAL INSTABILITY 95 6.3.3 DIFFERENT NUMERICAL DISCRETIZATIONS 98 6.3.4 DIFFERENT ATMOSPHERES 102 6.3.5 ARTIFICIAL PHYSICAL VISCOSITY 105 4 IMAGE 3 6.3.6 FIRE DYNAMICS SIMULATOR 107 6.3.7 CONCLUSIONS 108 6.4 INTERNAL GRAVITY WAVES 109 6.4.1 MOTION OF A DISPLACED FLUID ELEMENT 109 6.4.2 LINEAR THEORY IN BOUSSINESQ APPROXIMATION 110 6.4.3 SIMULATION OF A WAVE PACKET 112 6.4.4 NON-LINEAR BEHAVIOR AND ASTROPHYSICAL RELEVANCE 117 7 SHEAR INSTABILITIES 120 7.1 INTRODUCTION 120 7.2 MODEL PROBLEM 122 7.2.1 SETUP AND GOVERNING EQUATIONS 122 7.2.2 NON-DIMENSIONALIZATION 123 7.3 SEMI-ANALYTICAL STABILITY ANALYSIS 125 7.3.1 METHOD 125 7.3.2 RESULTS 126 7.4 2D SIMULATIONS 129 7.5 3D SIMULATION 133 8 SUMMARY AND OUTLOOK 139 A IMPLEMENTATION OF THE ROE-LOWMACH SCHEME 144 B BUTCHER TABLEAUS FOR ESDIRK SCHEMES 146 C TRANSFORMATIONS BETWEEN VARIABLES 148 D DETAILS OF THE SEMI-ANALYTICAL STABILITY ANALYSIS 150 5
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spelling	Miczek, Fabian Verfasser aut Simulation of low Mach number astrophysical flows Fabian Miczek 2013 156 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 (DE-588)4113937-9 Hochschulschrift gnd-content Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130508-1127720-0-4 http://mediatum.ub.tum.de/node?id=1127720 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130508-1127720-0-4 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026019706&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Miczek, Fabian Simulation of low Mach number astrophysical flows
subject_GND	(DE-588)4113937-9
title	Simulation of low Mach number astrophysical flows
title_auth	Simulation of low Mach number astrophysical flows
title_exact_search	Simulation of low Mach number astrophysical flows
title_full	Simulation of low Mach number astrophysical flows Fabian Miczek
title_fullStr	Simulation of low Mach number astrophysical flows Fabian Miczek
title_full_unstemmed	Simulation of low Mach number astrophysical flows Fabian Miczek
title_short	Simulation of low Mach number astrophysical flows
title_sort	simulation of low mach number astrophysical flows
topic_facet	Hochschulschrift
url	http://mediatum.ub.tum.de/node?id=1127720 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130508-1127720-0-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026019706&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT miczekfabian simulationoflowmachnumberastrophysicalflows

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