| Description |
1 online resource (xxiv, 483 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Summary |
Godunov-type schemes appear as good candidates for the next generation of commercial modelling software packages, the capability of which to handle discontinuous solution will be a basic requirement. It is in the interest of practising engineers and developers to be familiar with the specific features of discontinuous wave propagation problems and to be aware of the possibilities offered by Godunov-type schemes for their solution. This book aims to present the principles of such schemes in a way that is easily understandable to practising engineers. The features of hyperbolic conservation laws and their solutions are presented in the first two chapters. The principles of Godunov-type schemes are outlined in a third chapter. Chapters 4 and 5 cover the application of the original Godunov scheme to scalar laws and to hyperbolic systems of conservation laws respectively. Chapter 6 is devoted to higher-order schemes in one dimension of space. The design of such a scheme is described for the general case and applied to some well-known schemes such as the MUSCL and PPM schemes. Chapter 7 focuses on multidimensional problems. The classical alternate directions and finite volume approaches are presented together with the wave splitting technique that is described in depth with an application to two-dimensional systems. Chapter 8 deals with large-time step algorithms. These include front tracking-based methods, explicit-implicit techniques and the time-line interpolation technique. Three appendices provide notions on accuracy and stability issues, Riemann solvers and the user instructions for the computational codes provided in the enclosed CD-ROM. |
| Bibliography |
Includes bibliographical references (pages 471-480) and index. |
| Note |
Print version record. |
| Contents |
Cover -- Contents -- Preface -- Acknowledgements -- Notation -- VariabIes -- Operators -- Subscripts and superscripts -- Others -- Chapter 1. Scalar conservation laws -- 1.1 Definitions and basic notions -- 1.2 The Riemann problem -- 1.3 A linear conservation law: the advection equation -- 1.4 A convex conservation law: the Burgers equation -- 1.5 A concave conservation law: the LWR model -- 1.6 A non-convex conservation law: the Buckley-Leverett equation -- 1.7 Extension to multiple dimensions -- Chapter 2. Hyperbolic systems of conservation laws -- 2.1 Definitions -- 2.2 A linear system: the water hammer equations -- 2.3 Two-phase flow in pipes -- 2.4 A 2x2 model for traffic flow -- 2.5 The open channel flow equations with solute transport -- 2.6 The shallow water equations in two dimensions -- Chapter 3. An outline of Godunov-type schemes -- 3.1 The six steps of Godunov-type algorithms -- 3.2 Lagrangian schemes -- 3.3 Multidimensional problems -- 3.4 Stability constraints -- Chapter 4. The Godunov method for scalar laws in one dimension -- 4.1 The linear advection equation -- 4.2 Application to the inviscid Burgers equation -- 4.3 Application to the LWR model -- 4.4 Application to the Buckley-Leverett equation -- Chapter 5. The Godunov method for systems of conservation laws -- 5.1 Application to the water hammer equations -- 5.2 Application to the simplified model for two-phase flow in pipes -- 5.3 Application to a 2x2 traffic flow model -- 5.4 Application to the open channel flow equations -- Chapter 6. Higher-order schemes -- 6.1 Principle of higher-order schemes -- 6.2 The MUSCUPLM schemes -- 6.3 The PPM scheme -- 6.4 The DPM scheme -- 6.5 Boundary conditions for higher-order schemes -- 6.6 Application example -- Chapter 7. Multidimensional schemes -- 7.1 Multidimensional hyperbolic systems of conservation laws -- 7.2 Alternate directions -- 7.3 The finite volume approach -- 7.4 Wave splitting -- 7.5 Computational examples -- 7.6 Higher-order multidimensional schemes -- Chapter 8. Large-time-step algorithms -- 8.1 Front tracking algorithms -- 8.2 Implicit/explicit methods -- 8.3 The time-line reconstruction method -- 8.4 Computational examples -- Chapter 9. Concluding remarks -- Appendix A. Notions in mathematics -- A.1 Linear algebra -- A.2 Accuracy/consistency, stability, convergence -- Appendix B. Riemann solvers -- B.1 Exact Riemann solvers -- B.2 The HLL Riemann solver -- B.3 Roe's Riemann solver -- B.4 Approximate-state solvers -- Appendix C. Sample codes -- C.1 The code Linadv -- C.2 The code 'Burgers' -- C.3 The code 'LWR' -- C.4 The code 'BL' -- C.5 The code 'WatHam' -- C.6 The code '2phase' -- C.7 The code 'Traffic' -- C.8 The code 'Channel' -- C.9 The code 'Sh2D' -- C.10 The code 'Large' -- References -- Index -- L. |
| Subject |
Engineering mathematics.
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Differential equations, Hyperbolic -- Numerical solutions.
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Wave-motion, Theory of.
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Mathématiques de l'ingénieur.
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Équations différentielles hyperboliques -- Solutions numériques.
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Théorie du mouvement ondulatoire.
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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TECHNOLOGY & ENGINEERING -- Reference.
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Differential equations, Hyperbolic -- Numerical solutions
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Engineering mathematics
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Wave-motion, Theory of
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| Other Form: |
Print version: Guinot, Vincent. Godunov-type schemes. Amsterdam ; Boston : Elsevier, 2003 0444511555 9780444511553 (DLC) 2002043924 (OCoLC)51266078 |
| ISBN |
9780444511553 |
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0444511555 |
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9780080532585 (electronic bk.) |
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0080532586 (electronic bk.) |
| Standard No. |
AU@ 000062576019 |
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CHNEW 001006594 |
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DEBBG BV039831021 |
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DEBBG BV042315869 |
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DEBSZ 405309473 |
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NZ1 12433571 |
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NZ1 15191194 |
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