Godunov-type schemes : an introduction for engineers /

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 featur...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Guinot, Vincent
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; Boston : Elsevier, 2003.
Temas:
Engineering mathematics.
Differential equations, Hyperbolic > Numerical solutions.
Wave-motion, Theory of.
Math�ematiques de l'ing�enieur.
�Equations diff�erentielles hyperboliques > Solutions num�eriques.
Th�eorie du mouvement ondulatoire.
TECHNOLOGY & ENGINEERING > Engineering (General)
TECHNOLOGY & ENGINEERING > Reference.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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