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Handbook of Numerical Methods for Hyperbolic Problems : Basic and Fundamental Issues.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Saint Louis :
Elsevier Science,
2016.
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| Colección: | Handbook of numerical analysis.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Handbook of Numerical Methods for Hyperbolic Problems: Basic and Fundamental Issues; Copyright; Contents; Contributors; Introduction; Acknowledgements; Chapter 1: Introduction to the Theory of Hyperbolic Conservation Laws; 1. Introduction; 2. Basic Structure of Hyperbolic Conservation Laws; 3. Strictly Hyperbolic Systems in One Spatial Dimension; References; Chapter 2: The Riemann Problem: Solvers and Numerical Fluxes; 1. Preliminaries; 1.1. Definitions and Simple Examples; 1.2. Hyperbolic Systems and Finite Volume Methods.
- 2. Exact Solution of the Riemann Problem for the Euler Equations2.1. Equations and Structure of the Solution; 2.2. Pressure and Velocity in the Star Region; 2.3. The Complete Solution and the 3D Case; 2.4. Uses of the Exact Solution of the Riemann Problem; 2.5. Approximate Riemann Solvers: Beware; 3. The Roe Approximate Riemann Solver; 4. The HLL Approximate Riemann Solver; 5. The HLLC Approximate Riemann Solver; 5.1. Derivation of the HLLC Flux; 5.2. Wave Speed Estimates for HLL and HLLC; 6. A Numerical Version of the Osher-Solomon Riemann Solver.
- 7. Other Approaches to Constructing Numerical Fluxes8. Concluding Remarks; Acknowledgements; References; Chapter 3: Classical Finite Volume Methods; 1. Some Philosophical Remarks; 2. On the Lax-Wendroff Theorem; 3. Historical Remarks; 4. Weak Solutions and Finite Volume Methods; 5. The Cell-Centred Scheme of Jameson, Schmidt and Turkel; 6. Cell-Vertex Schemes on Quadrilateral Grids; 7. Finite Volume Methods on Unstructured Grids; 7.1. Cell-Centred Finite Volume Methods; 7.2. Vertex-Centred Finite Volume Methods; 7.3. Remarks on Recovery; References.
- Chapter 4: Sharpening Methods for Finite Volume Schemes1. Introduction; 2. Sharpening Methods for Linear Equations; 2.1. High-Order Methods; 2.2. Compression Within a BV Setting; 2.3. Inequality and Antidiffusion; 2.4. Glimm's Method; 2.5. PDE Models and Sharpening Methods; 2.6. Nature of the Grid/Mesh; 2.7. Interface Reconstruction and VOF; 2.8. Vofire; 3. Coupling With Hyperbolic Nonlinear Equations; 3.1. An Example of Discretization for Compressible Flows With Two Components Separated by a Sharp Interface; 3.2. Example of Other Evolution Equation Involving Sharp Interfaces.
- 3.3. Cut-Cells and CFL ConditionReferences; Chapter 5: ENO and WENO Schemes; 1. Introduction; 2. ENO and WENO Approximations; 2.1. Reconstruction; 2.2. ENO Approximation; 2.3. WENO Approximation; 3. ENO and WENO Schemes for Hyperbolic Conservation Laws; 3.1. Finite Volume Schemes; 3.2. Finite Difference Schemes; 3.3. Remarks on Multidimensional Problems and Systems; 4. Selected Topics of Recent Developments; 4.1. Unstructured Meshes; 4.2. Steady State Problems; 4.3. Time Discretizations for Convection-Diffusion Problems; 4.4. Accuracy Enhancement; Acknowledgements; References.