Finite volume methods for hyperbolic problems /:
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 phenomen...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2002.
|
| Schriftenreihe: | Cambridge texts in applied mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 resource (xix, 558 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 535-552) and index. |
| ISBN: | 0511042191 9780511042195 9780511791253 0511791259 0521810876 9780521810876 9780511045073 0511045077 0511148097 9780511148095 1107132460 9781107132467 1280419504 9781280419508 9786610419500 6610419507 0511177690 9780511177699 0511323638 9780511323638 |
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| 100 | 1 | |a LeVeque, Randall J., |d 1955- |1 https://id.oclc.org/worldcat/entity/E39PBJptV3jw4y6jhf78hjTj4q |0 http://id.loc.gov/authorities/names/n89116101 | |
| 245 | 1 | 0 | |a Finite volume methods for hyperbolic problems / |c Randall J. LeVeque. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2002. | ||
| 300 | |a 1 online resource (xix, 558 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Cambridge texts in applied mathematics | |
| 504 | |a Includes bibliographical references (pages 535-552) and index. | ||
| 505 | 0 | |a 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. | |
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a 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. | |
| 546 | |a English. | ||
| 650 | 0 | |a Differential equations, Hyperbolic |x Numerical solutions. |0 http://id.loc.gov/authorities/subjects/sh85037900 | |
| 650 | 0 | |a Finite volume method. |0 http://id.loc.gov/authorities/subjects/sh95001595 | |
| 650 | 0 | |a Conservation laws (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh90001934 | |
| 650 | 6 | |a Équations différentielles hyperboliques |x Solutions numériques. | |
| 650 | 6 | |a Méthodes de volumes finis. | |
| 650 | 6 | |a Lois de conservation (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
| 650 | 7 | |a Conservation laws (Mathematics) |2 fast | |
| 650 | 7 | |a Differential equations, Hyperbolic |x Numerical solutions |2 fast | |
| 650 | 7 | |a Finite volume method |2 fast | |
| 650 | 7 | |a Hyperbolische Differentialgleichung |2 gnd | |
| 650 | 7 | |a Finite-Volumen-Methode |2 gnd | |
| 650 | 7 | |a Erhaltungssatz |2 gnd | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 758 | |i has work: |a Finite volume methods for hyperbolic problems (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGhrjPmGd6cb9ppyx9p4C3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a LeVeque, Randall J., 1955- |t Finite volume methods for hyperbolic problems. |d Cambridge ; New York : Cambridge University Press, 2002 |z 0521810876 |z 0521009243 |w (DLC) 2001052642 |w (OCoLC)48221422 |
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| author | LeVeque, Randall J., 1955- |
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| contents | 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. |
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| genre | Electronic books. |
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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:15:34Z |
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| isbn | 0511042191 9780511042195 9780511791253 0511791259 0521810876 9780521810876 9780511045073 0511045077 0511148097 9780511148095 1107132460 9781107132467 1280419504 9781280419508 9786610419500 6610419507 0511177690 9780511177699 0511323638 9780511323638 |
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| spelling | LeVeque, Randall J., 1955- https://id.oclc.org/worldcat/entity/E39PBJptV3jw4y6jhf78hjTj4q http://id.loc.gov/authorities/names/n89116101 Finite volume methods for hyperbolic problems / Randall J. LeVeque. Cambridge ; New York : Cambridge University Press, 2002. 1 online resource (xix, 558 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file 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. Print version record. 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. English. Differential equations, Hyperbolic Numerical solutions. http://id.loc.gov/authorities/subjects/sh85037900 Finite volume method. http://id.loc.gov/authorities/subjects/sh95001595 Conservation laws (Mathematics) http://id.loc.gov/authorities/subjects/sh90001934 Équations différentielles hyperboliques Solutions numériques. Méthodes de volumes finis. 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 gnd Finite-Volumen-Methode gnd Erhaltungssatz gnd Electronic books. has work: Finite volume methods for hyperbolic problems (Text) https://id.oclc.org/worldcat/entity/E39PCGhrjPmGd6cb9ppyx9p4C3 https://id.oclc.org/worldcat/ontology/hasWork Print version: LeVeque, Randall J., 1955- Finite volume methods for hyperbolic problems. Cambridge ; New York : Cambridge University Press, 2002 0521810876 0521009243 (DLC) 2001052642 (OCoLC)48221422 Cambridge texts in applied mathematics. http://id.loc.gov/authorities/names/n86719346 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=112638 Volltext |
| spellingShingle | LeVeque, Randall J., 1955- Finite volume methods for hyperbolic problems / Cambridge texts in applied mathematics. 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. Differential equations, Hyperbolic Numerical solutions. http://id.loc.gov/authorities/subjects/sh85037900 Finite volume method. http://id.loc.gov/authorities/subjects/sh95001595 Conservation laws (Mathematics) http://id.loc.gov/authorities/subjects/sh90001934 Équations différentielles hyperboliques Solutions numériques. Méthodes de volumes finis. 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 gnd Finite-Volumen-Methode gnd Erhaltungssatz gnd |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037900 http://id.loc.gov/authorities/subjects/sh95001595 http://id.loc.gov/authorities/subjects/sh90001934 |
| 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. http://id.loc.gov/authorities/subjects/sh85037900 Finite volume method. http://id.loc.gov/authorities/subjects/sh95001595 Conservation laws (Mathematics) http://id.loc.gov/authorities/subjects/sh90001934 Équations différentielles hyperboliques Solutions numériques. Méthodes de volumes finis. 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 gnd Finite-Volumen-Methode gnd Erhaltungssatz gnd |
| topic_facet | Differential equations, Hyperbolic Numerical solutions. Finite volume method. Conservation laws (Mathematics) Équations différentielles hyperboliques Solutions numériques. Méthodes de volumes finis. Lois de conservation (Mathématiques) MATHEMATICS Differential Equations Partial. Differential equations, Hyperbolic Numerical solutions Finite volume method Hyperbolische Differentialgleichung Finite-Volumen-Methode Erhaltungssatz Electronic books. |
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