Systems of Conservation Laws: Two-Dimensional Riemann Problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2001
|
| Schriftenreihe: | Progress in Nonlinear Differential Equations and Their Applications
38 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This work is based on the lecture notes of the course M742: Topics in Partial Differential Equations, which I taught in the Spring semester of 1997 at Indiana University. My main intention in this course was to give a concise introduction to solving two-dimensional compressible Euler equations with Riemann data, which are special Cauchy data. This book covers new theoretical developments in the field over the past decade or so. Necessary knowledge of one-dimensional Riemann problems is reviewed and some popular numerical schemes are presented. Multi-dimensional conservation laws are more physical and the time has come to study them. The theory on basic one-dimensional conservation laws isfairly complete providing solid foundation for multi-dimensional problems. The rich theory on elliptic and parabolic partial differential equations has great potential in applications to multi-dimensional conservation laws. And faster computers make it possible to reveal numerically more details for theoretical pursuit in multi-dimensional problems. Overview and highlights Chapter 1 is an overview of the issues that concern us in this book. It lists the Euler system and related models such as the unsteady transonic small disturbance, pressure-gradient, and pressureless systems. It describes Mach reflection and the von Neumann paradox. In Chapters 2-4, which form Part I of the book, we briefly present the theory of one-dimensional conservation laws, which includes solutions to the Riemann problems for the Euler system and general strictly hyperbolic and genuinely nonlinear systems, Glimm's scheme, and large-time asymptoties |
| Beschreibung: | 1 Online-Ressource (XV, 320 p) |
| ISBN: | 9781461201410 9781461266310 |
| DOI: | 10.1007/978-1-4612-0141-0 |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Zheng, Yuxi |
| author_facet | Zheng, Yuxi |
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| author_sort | Zheng, Yuxi |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0141-0 |
| format | Electronic eBook |
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| id | DE-604.BV042419451 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781461201410 9781461266310 |
| language | English |
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| series | Progress in Nonlinear Differential Equations and Their Applications |
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| spelling | Zheng, Yuxi Verfasser aut Systems of Conservation Laws Two-Dimensional Riemann Problems by Yuxi Zheng Boston, MA Birkhäuser Boston 2001 1 Online-Ressource (XV, 320 p) txt rdacontent c rdamedia cr rdacarrier Progress in Nonlinear Differential Equations and Their Applications 38 This work is based on the lecture notes of the course M742: Topics in Partial Differential Equations, which I taught in the Spring semester of 1997 at Indiana University. My main intention in this course was to give a concise introduction to solving two-dimensional compressible Euler equations with Riemann data, which are special Cauchy data. This book covers new theoretical developments in the field over the past decade or so. Necessary knowledge of one-dimensional Riemann problems is reviewed and some popular numerical schemes are presented. Multi-dimensional conservation laws are more physical and the time has come to study them. The theory on basic one-dimensional conservation laws isfairly complete providing solid foundation for multi-dimensional problems. The rich theory on elliptic and parabolic partial differential equations has great potential in applications to multi-dimensional conservation laws. And faster computers make it possible to reveal numerically more details for theoretical pursuit in multi-dimensional problems. Overview and highlights Chapter 1 is an overview of the issues that concern us in this book. It lists the Euler system and related models such as the unsteady transonic small disturbance, pressure-gradient, and pressureless systems. It describes Mach reflection and the von Neumann paradox. In Chapters 2-4, which form Part I of the book, we briefly present the theory of one-dimensional conservation laws, which includes solutions to the Riemann problems for the Euler system and general strictly hyperbolic and genuinely nonlinear systems, Glimm's scheme, and large-time asymptoties Mathematics Global analysis (Mathematics) Computer science / Mathematics Analysis Applications of Mathematics Computational Mathematics and Numerical Analysis Informatik Mathematik Hyperbolisches System (DE-588)4191897-6 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Riemannsches Problem (DE-588)4243352-6 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 s Hyperbolisches System (DE-588)4191897-6 s Riemannsches Problem (DE-588)4243352-6 s 1\p DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Strömungsmechanik (DE-588)4077970-1 s 2\p DE-604 Progress in Nonlinear Differential Equations and Their Applications 38 (DE-604)BV036582883 38 https://doi.org/10.1007/978-1-4612-0141-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zheng, Yuxi Systems of Conservation Laws Two-Dimensional Riemann Problems Progress in Nonlinear Differential Equations and Their Applications Mathematics Global analysis (Mathematics) Computer science / Mathematics Analysis Applications of Mathematics Computational Mathematics and Numerical Analysis Informatik Mathematik Hyperbolisches System (DE-588)4191897-6 gnd Erhaltungssatz (DE-588)4131214-4 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd Riemannsches Problem (DE-588)4243352-6 gnd |
| subject_GND | (DE-588)4191897-6 (DE-588)4131214-4 (DE-588)4044779-0 (DE-588)4077970-1 (DE-588)4243352-6 |
| title | Systems of Conservation Laws Two-Dimensional Riemann Problems |
| title_auth | Systems of Conservation Laws Two-Dimensional Riemann Problems |
| title_exact_search | Systems of Conservation Laws Two-Dimensional Riemann Problems |
| title_full | Systems of Conservation Laws Two-Dimensional Riemann Problems by Yuxi Zheng |
| title_fullStr | Systems of Conservation Laws Two-Dimensional Riemann Problems by Yuxi Zheng |
| title_full_unstemmed | Systems of Conservation Laws Two-Dimensional Riemann Problems by Yuxi Zheng |
| title_short | Systems of Conservation Laws |
| title_sort | systems of conservation laws two dimensional riemann problems |
| title_sub | Two-Dimensional Riemann Problems |
| topic | Mathematics Global analysis (Mathematics) Computer science / Mathematics Analysis Applications of Mathematics Computational Mathematics and Numerical Analysis Informatik Mathematik Hyperbolisches System (DE-588)4191897-6 gnd Erhaltungssatz (DE-588)4131214-4 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd Riemannsches Problem (DE-588)4243352-6 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Computer science / Mathematics Analysis Applications of Mathematics Computational Mathematics and Numerical Analysis Informatik Mathematik Hyperbolisches System Erhaltungssatz Partielle Differentialgleichung Strömungsmechanik Riemannsches Problem |
| url | https://doi.org/10.1007/978-1-4612-0141-0 |
| volume_link | (DE-604)BV036582883 |
| work_keys_str_mv | AT zhengyuxi systemsofconservationlawstwodimensionalriemannproblems |