Finite volume methods for hyperbolic problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2002
|
| Schriftenreihe: | Cambridge texts in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 535-552) and index Conservation laws and differential equations -- Characteristics and Riemann problems for linear hyperbolic equations -- Finite-volume methods -- Introduction to the CLAWPACK software -- High resolution methods -- Boundary conditions and ghost cells -- Convergence, accuracy, and stability -- Variable-coefficient linear equations -- Other approaches to high resolution -- Nonlinear scalar conservation laws -- Finite-volume methods for nonlinear scalar conservation laws -- Nonlinear systems of conservation laws -- Gas dynamics and the Euler equations -- Finite-volume methods for nonlinear systems -- Some nonclassical hyperbolic problems -- Source terms and balance laws -- Multidimensional hyperbolic problems -- Multidimensional numerical methods -- Multidimensional scalar equations -- Multidimensional systems -- Elastic waves -- Finite-volume methods on quadrilateral grids This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods |
| Beschreibung: | 1 Online-Ressource (xix, 558 pages) |
| ISBN: | 0511042191 0511791259 0521009243 0521810876 9780511042195 9780511791253 9780521009249 9780521810876 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | LeVeque, Randall J. |
| author_facet | LeVeque, Randall J. |
| author_role | aut |
| author_sort | LeVeque, Randall J. |
| author_variant | r j l rj rjl |
| building | Verbundindex |
| bvnumber | BV043159184 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043159184 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:18Z |
| institution | BVB |
| isbn | 0511042191 0511791259 0521009243 0521810876 9780511042195 9780511791253 9780521009249 9780521810876 |
| language | English |
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| spelling | LeVeque, Randall J. Verfasser aut Finite volume methods for hyperbolic problems Randall J. LeVeque Cambridge Cambridge University Press 2002 1 Online-Ressource (xix, 558 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge texts in applied mathematics Includes bibliographical references (pages 535-552) and index Conservation laws and differential equations -- Characteristics and Riemann problems for linear hyperbolic equations -- Finite-volume methods -- Introduction to the CLAWPACK software -- High resolution methods -- Boundary conditions and ghost cells -- Convergence, accuracy, and stability -- Variable-coefficient linear equations -- Other approaches to high resolution -- Nonlinear scalar conservation laws -- Finite-volume methods for nonlinear scalar conservation laws -- Nonlinear systems of conservation laws -- Gas dynamics and the Euler equations -- Finite-volume methods for nonlinear systems -- Some nonclassical hyperbolic problems -- Source terms and balance laws -- Multidimensional hyperbolic problems -- Multidimensional numerical methods -- Multidimensional scalar equations -- Multidimensional systems -- Elastic waves -- Finite-volume methods on quadrilateral grids This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods Differential equations, Hyperbolic / Numerical solutions Finite volume method Conservation laws (Mathematics) Équations différentielles hyperboliques / Solutions numériques Volumes finis, Méthodes de Lois de conservation (Mathématiques) MATHEMATICS / Differential Equations / Partial bisacsh Conservation laws (Mathematics) fast Differential equations, Hyperbolic / Numerical solutions fast Finite volume method fast Hyperbolische Differentialgleichung swd Finite-Volumen-Methode swd Erhaltungssatz swd Differential equations, Hyperbolic Numerical solutions Hyperbolisches System (DE-588)4191897-6 gnd rswk-swf Finite-Volumen-Methode (DE-588)4220855-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Hyperbolisches System (DE-588)4191897-6 s Finite-Volumen-Methode (DE-588)4220855-5 s 1\p DE-604 Hyperbolische Differentialgleichung (DE-588)4131213-2 s Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=112638 Aggregator 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 | LeVeque, Randall J. Finite volume methods for hyperbolic problems Differential equations, Hyperbolic / Numerical solutions Finite volume method Conservation laws (Mathematics) Équations différentielles hyperboliques / Solutions numériques Volumes finis, Méthodes de Lois de conservation (Mathématiques) MATHEMATICS / Differential Equations / Partial bisacsh Conservation laws (Mathematics) fast Differential equations, Hyperbolic / Numerical solutions fast Finite volume method fast Hyperbolische Differentialgleichung swd Finite-Volumen-Methode swd Erhaltungssatz swd Differential equations, Hyperbolic Numerical solutions Hyperbolisches System (DE-588)4191897-6 gnd Finite-Volumen-Methode (DE-588)4220855-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| subject_GND | (DE-588)4191897-6 (DE-588)4220855-5 (DE-588)4128130-5 (DE-588)4131213-2 |
| title | Finite volume methods for hyperbolic problems |
| title_auth | Finite volume methods for hyperbolic problems |
| title_exact_search | Finite volume methods for hyperbolic problems |
| title_full | Finite volume methods for hyperbolic problems Randall J. LeVeque |
| title_fullStr | Finite volume methods for hyperbolic problems Randall J. LeVeque |
| title_full_unstemmed | Finite volume methods for hyperbolic problems Randall J. LeVeque |
| title_short | Finite volume methods for hyperbolic problems |
| title_sort | finite volume methods for hyperbolic problems |
| topic | Differential equations, Hyperbolic / Numerical solutions Finite volume method Conservation laws (Mathematics) Équations différentielles hyperboliques / Solutions numériques Volumes finis, Méthodes de Lois de conservation (Mathématiques) MATHEMATICS / Differential Equations / Partial bisacsh Conservation laws (Mathematics) fast Differential equations, Hyperbolic / Numerical solutions fast Finite volume method fast Hyperbolische Differentialgleichung swd Finite-Volumen-Methode swd Erhaltungssatz swd Differential equations, Hyperbolic Numerical solutions Hyperbolisches System (DE-588)4191897-6 gnd Finite-Volumen-Methode (DE-588)4220855-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| topic_facet | Differential equations, Hyperbolic / Numerical solutions Finite volume method Conservation laws (Mathematics) Équations différentielles hyperboliques / Solutions numériques Volumes finis, Méthodes de Lois de conservation (Mathématiques) MATHEMATICS / Differential Equations / Partial Hyperbolische Differentialgleichung Finite-Volumen-Methode Erhaltungssatz Differential equations, Hyperbolic Numerical solutions Hyperbolisches System Numerisches Verfahren |
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| work_keys_str_mv | AT levequerandallj finitevolumemethodsforhyperbolicproblems |