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Finite Volume Methods for Hyperbolic Problems
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TLDR
The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.Abstract:
Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.read more
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References
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A perfectly matched layer for the absorption of electromagnetic waves
TL;DR: Numerical experiments and numerical comparisons show that the PML technique works better than the others in all cases; using it allows to obtain a higher accuracy in some problems and a release of computational requirements in some others.
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Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
Book
Riemann Solvers and Numerical Methods for Fluid Dynamics
TL;DR: In this article, the authors present references and index Reference Record created on 2004-09-07, modified on 2016-08-08 and a reference record created on 2003-09 -07.
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Efficient Implementation of Weighted ENO Schemes
Guang-Shan Jiang,Chi-Wang Shu +1 more
TL;DR: A new way of measuring the smoothness of a numerical solution is proposed, emulating the idea of minimizing the total variation of the approximation, which results in a fifth-order WENO scheme for the caser= 3, instead of the fourth-order with the original smoothness measurement by Liuet al.
Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu,Stanley Osher +1 more
TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.