Godunov Methods Theory and Applications

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.

Oleinik's E-Condition from the Viewpoint of Numerics; H. Aiso. On Some New Results for Residual Distribution Schemes; R. Abgrall, T.J. Barth. Simulations of Relativistic Jets with Genesis; M.A. Aloy, et al. Relativistic Jets from Collapsars; M.A. Aloy, et al. Exact Computation in Numerical Linear Algebra: The Discrete Fourier Transform; J.A.D.W. Anderson, P.K. Sweby. Comparative Study of HLL, HLLC and Hybrid Riemann Solvers in Unsteady Compressible Flows; A. Bagabir, D. Drikakis. A New Reconstruction Technique for the Euler Equations of Gas Dynamics with Source Terms; P. Bartsch, A. Borzi. Colella-Glaz Splitting Scheme for Thermally Perfect Gases; A. Beccantini. Meshless Particle Methods: Recent Developments for Nonlinear Conservation Laws in Bounded Domain; B.B. Moussa. Application of Wave-propagation Algorithm to Two-dimensional Thermoelastic Wave Propagation in Inhomogeneous Media; A. Berezovski, G.A. Maugin. Unstructured Mesh Solvers for Hyperbolic PDEs with Source Terms: Error Estimates and Mesh Quality; M. Berzins, L.J.K. Durbeck. Constancy Preserving, Conservative Methods for Free-surface Models; L. Bonaventura, E. Gross. Hyperbolic-elliptic Splitting for the Pseudo-compressible Euler Equations; A. Bonfiglioli. Godunov Solution of Shallow Water Equations on Curvilinear and Quadtree Grids; A.G.L. Borthwick, et al. A High-order-accurate Reconstruction for the Computation of Compressible Flows on Cell-vertex Triangular Grids; L.A. Catalano. Numerical Experiments with Multilevel Schemes for Conservation Laws; G. Chiavassa, R. Donat. Volume-of-fluid Methods for Partial Differential Equations; P. Colella. Some New Godunov and Related Relaxation Methods for Two-phase Flow Problems; F. Coquel, et al. Development of Genuinely Multi-dimensional Upwind Residual Distribution Schemes for the System of Eight Wave Ideal Magnetohydrodynamic Equations on Uncunstructured Grids; A. Csík, et al. Application of TVD High Resolution Schemes to the Viscous Shock Tube Problem; V. Daru, C. Tenaud. Comparison of Numerical Solvers with Godunov Scheme for Multicomponent Turbulent Flows; E. Declercq. Godunov-type Schemes for the MHD Equations; A. Dedner, et al. Absorbing Boundary Conditions for Astrophysical MHD Simulations; A. Dedner, et al. About Kinetic Schemes Built in Axisymmetrical and Spherical Geometries; S. Dellacherie. Lagrangian Systems of Conservation Laws and Approximate Riemann Solvers; B. Després. Intermediate Shocks in 3D MHD Bow Shock Flows; H. De Sterck, S. Poedts. A Second Order Godunov-type Scheme for Naval Hydrodynamics; A. Di Mascio, et al. Uniformly High-order Methods for Unsteady Incompressible Flows; D. Drikakis. Application of the Finite Volume Method with Osher Scheme and Split Technique for Different Types of Flow in a Channel; K.S. Erduran, V. Kutija. A-priori Estimates for a Semi-Lagrangian Scheme for the Wave Equation; M. Falcone, R. Ferretti. Interstellar Shock Structures in Weakly Ionised Gases; S.A.G.E. Falle. The Ghost Fluid Method for Numerical Treatment of Discontinuities and Interfaces; R.P. Fedkiw. A Hybrid Primitive-Conservative Upwind Scheme for the Drift Flux Model; K.K. Fjelde, K.H. Karlsen. Numerical Simulations of Relativistic Wind Accretion onto Black Holes Using Godunov-type Methods; J.A. Font, et al. A Second Order Accurate, Space-time Limited, BDF Scheme for the Linear Advection Equation; S.A. Forth. Multidimensional Upwind Schemes: Application to Hydraulics; P. Garcia-Navarro, et al.