Godunov Methods

1. Front Matter

   Pages i-xvii

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2. OleĬnik’s E-Condition from the Viewpoint of Numerics

   • Hideaki Aiso

   Pages 1-25

3. New Results for Residual Distribution Schemes

   • R. Abgrall, T. J. Barth

   Pages 27-43

4. Simulations of Relativistic Jets with Genesis

   • M. A. Aloy, J. M. Ibanyez, J. M. Marti, J. L. Gomez, E. Mueller

   Pages 45-52

5. Relativistic Jets from Collapsars

   • M. A. Aloy, E. Mueller, J. M. Ibanyez, J. M. Marti, A. Macfadyen

   Pages 53-59

6. Exact Computation in Numerical Linear Algebra: The Discrete Fourier Transform

   • J. A. D. W. Anderson, P. K. Sweby

   Pages 61-67

7. Comparative Study of HLL, HLLC and Hybrid Riemann Solvers in Unsteady Compressible Flows

   • A. Bagabir, D. Drikakis

   Pages 69-75

8. A New Reconstruction Technique for the Euler Equations of Gas Dynamics with Source Terms

   • P. Bartsch, A. Borzi’

   Pages 77-88

9. Colella-Glaz Splitting Scheme for Thermally Perfect Gases

   • A. Beccantini

   Pages 89-95

10. Meshless Particle Methods: Recent Developments for Nonlinear Conservation Laws in Bounded Domain

    • B. Ben Moussa

    Pages 97-108

11. Application of Wave-Propagation Algorithm to Two-Dimensional Thermoelastic Wave Propagation in Inhomogeneous Media

    • A. Berezovski, G. A. Maugin

    Pages 109-116

12. Unstructured Mesh Solvers for Hyperbolic PDES with Source Terms: Error Estimates and Mesh Quality

    • M. Berzins, L. J. K. Durbeck

    Pages 117-123

13. Constancy Preserving, Conservative Methods for Free-Surface Models

    • L. Bonaventura, E. S. Gross

    Pages 125-133

14. Hyperbolic-Elliptic Splitting for the Pseudo-Compressible Euler Equations

    • A. Bonfiglioli

    Pages 135-140

15. Godunov Solution of Shallow Water Equations on Curvilinear and Quadtree Grids

    • A. G. L. Borthwick, M. Fujihara, B. D. Rogers

    Pages 141-148

16. A Higher-Order-Accurate Reconstruction for the Computation of Compressible Flows on Cell-Vertex Triangular Grids

    • L. A. Catalano

    Pages 149-154

17. Numerical Experiments with Multilevel Schemes for Conservation Laws

    • G. Chiavassa, R. Donat

    Pages 155-160

18. Volume-of-Fluid Methods for Partial Differential Equations

    • Phillip Colella

    Pages 161-177

19. Some New Godunov and Relaxation Methods for Two-Phase Flow Problems

    • F. Coquel, E. Godlewski, B. Perthame, A. In, P. Rascle

    Pages 179-188

20. Development of Genuinely Multidimensional Upwind Residual Distribution Schemes for the System of Eight Wave Ideal Magnetohydro-Dynamic Equations on Unstructured Grids

    • Árpád Csík, Herman Deconinck, Stefaan Poedts

    Pages 189-196

This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo­ rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu­ ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at­ tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol­ lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.

• Mathematica
• algorithms
• discrete Fourier transform
• geometry
• hyperbolic partial differential equation
• numerical methods
• partial differential equation
• simulation
• wave equation

• Manchester Metropolitan University, Manchester, UK

  E. F. Toro

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