Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Würzburg
Würzburg University Press
[2023]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiv, 137 Seiten Illustrationen, Diagramme |
| ISBN: | 9783958262102 3958262104 9783958262119 |
Internformat
MARC
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| 100 | 1 | |a Kanbar, Farah |e Verfasser |0 (DE-588)1289546029 |4 aut | |
| 245 | 1 | 0 | |a Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations |c Farah Kanbar |
| 264 | 1 | |a Würzburg |b Würzburg University Press |c [2023] | |
| 264 | 4 | |c © 2023 | |
| 300 | |a xiv, 137 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |b Dissertation |c Würzburg, Julius-Maximilians-Universität Würzburg |d 2022 | ||
| 653 | |a Angewandte Mathematik | ||
| 653 | |a Hyperbolische Differentialgleichung | ||
| 653 | |a Kinetische Gleichung | ||
| 653 | |a Euler-Lagrange-Gleichung | ||
| 653 | |a Magnetohydrodynamische Gleichung | ||
| 653 | |a Euler equations | ||
| 653 | |a isentropic Euler equations | ||
| 653 | |a MHD equations | ||
| 653 | |a kinetic equations | ||
| 653 | |a well-balanced scheme | ||
| 653 | |a asymptotic preserving | ||
| 653 | |a stationary preserving | ||
| 653 | |a hyperbolic partial differential equations | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 710 | 2 | |a Würzburg University Press |0 (DE-588)1068107367 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |a Kanbar, Farah |t Asymptotic and Stationary Preserving Schemes for Kinetic and Hyperbolic Partial Differential Equations |d Würzburg : Würzburg University Press, 2023 |z 978-3-95826-211-9 |o 10.25972/WUP-978-3-95826-211-9 |w (DE-604)BV048963589 |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034295335&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-034295335 | ||
| 883 | 1 | |8 1\p |a vlb |d 20230511 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
Datensatz im Suchindex
| _version_ | 1804185318252871680 |
|---|---|
| adam_text | CONTENTS
ACKNOWLEDGMENTS
V
PREFACE
VII
ABSTRACT
IX
ABBREVIATIONS
XI
1
INTRODUCTION
1
2
WELL-BALANCED
CENTRAL
SCHEMES
WITH
THE
SUBTRACTION
METHOD
5
2.1
INTRODUCTION
.....................................................................................................
5
2.2
1
D
UNSTAGGERED
WELL-BALANCED
FV
CENTRAL
SCHEME
.......................................
5
2.3
2D
UNSTAGGERED
WELL-BALANCED
FV
CENTRAL
SCHEME
.......................................
13
2.4
TVD
PROPERTY
OF
THE
SCHEME
APPLIED
TO
SCALAR
CONSERVATION
LAW
...............
19
2.5
NUMERICAL
RESULTS
.........................................................................................
23
2.5.1
APPLICATION
TO
THE
1
D
EULER
SYSTEM
WITH
GRAVITATIONAL
SOURCE
TERM
...
23
2.5.2
APPLICATION
TO
THE
2D
EULER
SYSTEM
WITH
GRAVITATIONAL
SOURCE
TERM
...
26
2.5.3
APPLICATION
TO
THE
2D
MHD
EQUATIONS
WITH
GRAVITATIONAL
SOURCE
TERM
.
.
29
2.5.4
MHD
WAVE
PROPAGATION-WEAK
MAGNETIC
FIELD
.............................
37
2.6
CONCLUSION
....................................................................................................
38
3
AP
AND
SP
SCHEMES
FOR
KINETIC
EQUATIONS
61
3.1
INTRODUCTION
.....................................................................................................
61
3.2
PARITY
EQUATIONS-BASED
SCHEME
FOR
THE
NEUTRON
TRANSPORT
EQUATION
...............
62
3.2.1
THE
NEUTRON
TRANSPORT
EQUATION
...........................................................
62
3.2.2
DISCRETIZATION
OF
THE
MODEL
.................................................................
62
3.2.3
SP
PROPERTY
.........................................................................................
64
3.2.4
NUMERICAL
RESULTS
................................................................................
66
3.3
UGKS
SCHEME
FOR
THE
CHEMOTAXIS
KINETIC
MODEL
.............................................
66
3.3.1
THE
CHEMOTAXIS
KINETIC
MODEL
...........................................................
67
3.3.2
DISCRETIZATION
OF
THE
MODEL
.................................................................
67
3.3.3
SP
PROPERTY
.........................................................................................
70
3.3.4
NUMERICAL
RESULTS
................................................................................
71
3.4
IMEX
SCHEME
WITH
THE
PENALIZATION
METHOD
FOR
THE
BOLTZMANN
EQUATION
.
.
.
72
3.4.1
THE
BOLTZMANN
EQUATION
....................................................................
72
3.4.2
IMEX
SCHEME
WITH
THE
PENALIZATION
METHOD
......................................
73
3.4.3
SP
PROPERTY
.........................................................................................
73
3.4.4
NUMERICAL
RESULTS
................................................................................
74
3.5
CONCLUSION
.....................................................................................................
75
4
AP
AND
SP
SCHEMES
FOR
THE
ISENTROPIC
EULER
EQUATIONS
WITH
GRAVITY
83
4.1
INTRODUCTION
.......................................................................................................
83
4.2
THE
ISENTROPIC
EULER
EQUATIONS
WITH
GRAVITY
....................................................
83
4.2.1
THE
MODEL
............................................................................................
83
4.2.2
SCALING
..................................................................................................
83
4.2.3
THE
INCOMPRESSIBLE
LIMIT
EQUATIONS
........................................................
85
4.3
SEMI-DISCRETE
NUMERICAL
SCHEME
...................................................................
86
4.3.1
THE
SCHEME
...........................................................................................
86
4.3.2
THE
AP
PROPERTY
..................................................................................
87
4.4
FULLY
DISCRETE
NUMERICAL
SCHEME
...................................................................
91
4.4.1
THE
1D
NUMERICAL
SCHEME
...................................................................
92
4.4.2
THE
2D
NUMERICAL
SCHEME
...................................................................
95
4.4.3
THE
AP
PROPERTY
FOR
THE
2D
NUMERICAL
SCHEME
.......................................
103
4.4.4
THE
SP
PROPERTY
OF
THE
2D
NUMERICAL
SCHEME
........................................
107
4.5
NUMERICAL
RESULTS
............................................................................................
107
4.5.1
1D
TEST
CASES
..........................................................................................
108
4.5.2
2D
TEST
CASES
..........................................................................................
110
4.6
CONCLUSION
........................................................................................................
114
5
CONCLUSION
AND
FUTURE
WORK
125
6
APPENDICES
127
BIBLIOGRAPHY
131
|
| adam_txt |
CONTENTS
ACKNOWLEDGMENTS
V
PREFACE
VII
ABSTRACT
IX
ABBREVIATIONS
XI
1
INTRODUCTION
1
2
WELL-BALANCED
CENTRAL
SCHEMES
WITH
THE
SUBTRACTION
METHOD
5
2.1
INTRODUCTION
.
5
2.2
1
D
UNSTAGGERED
WELL-BALANCED
FV
CENTRAL
SCHEME
.
5
2.3
2D
UNSTAGGERED
WELL-BALANCED
FV
CENTRAL
SCHEME
.
13
2.4
TVD
PROPERTY
OF
THE
SCHEME
APPLIED
TO
SCALAR
CONSERVATION
LAW
.
19
2.5
NUMERICAL
RESULTS
.
23
2.5.1
APPLICATION
TO
THE
1
D
EULER
SYSTEM
WITH
GRAVITATIONAL
SOURCE
TERM
.
23
2.5.2
APPLICATION
TO
THE
2D
EULER
SYSTEM
WITH
GRAVITATIONAL
SOURCE
TERM
.
26
2.5.3
APPLICATION
TO
THE
2D
MHD
EQUATIONS
WITH
GRAVITATIONAL
SOURCE
TERM
.
.
29
2.5.4
MHD
WAVE
PROPAGATION-WEAK
MAGNETIC
FIELD
.
37
2.6
CONCLUSION
.
38
3
AP
AND
SP
SCHEMES
FOR
KINETIC
EQUATIONS
61
3.1
INTRODUCTION
.
61
3.2
PARITY
EQUATIONS-BASED
SCHEME
FOR
THE
NEUTRON
TRANSPORT
EQUATION
.
62
3.2.1
THE
NEUTRON
TRANSPORT
EQUATION
.
62
3.2.2
DISCRETIZATION
OF
THE
MODEL
.
62
3.2.3
SP
PROPERTY
.
64
3.2.4
NUMERICAL
RESULTS
.
66
3.3
UGKS
SCHEME
FOR
THE
CHEMOTAXIS
KINETIC
MODEL
.
66
3.3.1
THE
CHEMOTAXIS
KINETIC
MODEL
.
67
3.3.2
DISCRETIZATION
OF
THE
MODEL
.
67
3.3.3
SP
PROPERTY
.
70
3.3.4
NUMERICAL
RESULTS
.
71
3.4
IMEX
SCHEME
WITH
THE
PENALIZATION
METHOD
FOR
THE
BOLTZMANN
EQUATION
.
.
.
72
3.4.1
THE
BOLTZMANN
EQUATION
.
72
3.4.2
IMEX
SCHEME
WITH
THE
PENALIZATION
METHOD
.
73
3.4.3
SP
PROPERTY
.
73
3.4.4
NUMERICAL
RESULTS
.
74
3.5
CONCLUSION
.
75
4
AP
AND
SP
SCHEMES
FOR
THE
ISENTROPIC
EULER
EQUATIONS
WITH
GRAVITY
83
4.1
INTRODUCTION
.
83
4.2
THE
ISENTROPIC
EULER
EQUATIONS
WITH
GRAVITY
.
83
4.2.1
THE
MODEL
.
83
4.2.2
SCALING
.
83
4.2.3
THE
INCOMPRESSIBLE
LIMIT
EQUATIONS
.
85
4.3
SEMI-DISCRETE
NUMERICAL
SCHEME
.
86
4.3.1
THE
SCHEME
.
86
4.3.2
THE
AP
PROPERTY
.
87
4.4
FULLY
DISCRETE
NUMERICAL
SCHEME
.
91
4.4.1
THE
1D
NUMERICAL
SCHEME
.
92
4.4.2
THE
2D
NUMERICAL
SCHEME
.
95
4.4.3
THE
AP
PROPERTY
FOR
THE
2D
NUMERICAL
SCHEME
.
103
4.4.4
THE
SP
PROPERTY
OF
THE
2D
NUMERICAL
SCHEME
.
107
4.5
NUMERICAL
RESULTS
.
107
4.5.1
1D
TEST
CASES
.
108
4.5.2
2D
TEST
CASES
.
110
4.6
CONCLUSION
.
114
5
CONCLUSION
AND
FUTURE
WORK
125
6
APPENDICES
127
BIBLIOGRAPHY
131 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kanbar, Farah |
| author_GND | (DE-588)1289546029 |
| author_facet | Kanbar, Farah |
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| author_sort | Kanbar, Farah |
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| building | Verbundindex |
| bvnumber | BV049032674 |
| classification_rvk | SK 920 |
| ctrlnum | (OCoLC)1381934954 (DE-599)DNB1289090343 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV049032674 |
| illustrated | Illustrated |
| index_date | 2024-07-03T22:17:08Z |
| indexdate | 2024-07-10T09:53:20Z |
| institution | BVB |
| institution_GND | (DE-588)1068107367 |
| isbn | 9783958262102 3958262104 9783958262119 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034295335 |
| oclc_num | 1381934954 |
| open_access_boolean | |
| owner | DE-20 DE-12 |
| owner_facet | DE-20 DE-12 |
| physical | xiv, 137 Seiten Illustrationen, Diagramme |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Würzburg University Press |
| record_format | marc |
| spelling | Kanbar, Farah Verfasser (DE-588)1289546029 aut Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations Farah Kanbar Würzburg Würzburg University Press [2023] © 2023 xiv, 137 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Dissertation Würzburg, Julius-Maximilians-Universität Würzburg 2022 Angewandte Mathematik Hyperbolische Differentialgleichung Kinetische Gleichung Euler-Lagrange-Gleichung Magnetohydrodynamische Gleichung Euler equations isentropic Euler equations MHD equations kinetic equations well-balanced scheme asymptotic preserving stationary preserving hyperbolic partial differential equations (DE-588)4113937-9 Hochschulschrift gnd-content Würzburg University Press (DE-588)1068107367 pbl Erscheint auch als Online-Ausgabe, PDF Kanbar, Farah Asymptotic and Stationary Preserving Schemes for Kinetic and Hyperbolic Partial Differential Equations Würzburg : Würzburg University Press, 2023 978-3-95826-211-9 10.25972/WUP-978-3-95826-211-9 (DE-604)BV048963589 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034295335&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20230511 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Kanbar, Farah Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations |
| subject_GND | (DE-588)4113937-9 |
| title | Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations |
| title_auth | Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations |
| title_exact_search | Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations |
| title_exact_search_txtP | Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations |
| title_full | Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations Farah Kanbar |
| title_fullStr | Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations Farah Kanbar |
| title_full_unstemmed | Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations Farah Kanbar |
| title_short | Asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations |
| title_sort | asymptotic and stationary preserving schemes for kinetic and hyperbolic partial differential equations |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034295335&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kanbarfarah asymptoticandstationarypreservingschemesforkineticandhyperbolicpartialdifferentialequations AT wurzburguniversitypress asymptoticandstationarypreservingschemesforkineticandhyperbolicpartialdifferentialequations |