Overview

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 commemorate the 70th birthday of the Russian mathematician Sergei K. Godunov. The central theme of this book is numerical methods for hyperbolic conservation laws following Godunov's key ideas contained in his celebrated paper of 1959. Hyperbolic conservation laws play a central role in mathematical modelling in several distinct disciplines of science and technology. Application areas include compressible, single (and multiple) fluid dynamics, shock waves, meteorology, elasticity, magnetohydrodynamics, relativity, and many others. The successes in the design and application of new and improved numerical methods of the Godunov type for hyperbolic conservation laws in the last twenty years have made a dramatic impact in these application areas. The 97 papers cover a very wide range of topics, such as design and analysis of numerical schemes, applications to compressible and incompressible fluid dynamics, multi-phase flows, combustion problems, astrophysics, environmental fluid dynamics, and detonation waves. All contributions are self-contained but do contain a review element. There is a key paper by Peter Sweby in which a general overview of Godunov methods is given. This contribution is particularly suitable for beginners on the subject. This book contains virtually everything concerned with Godunov-type methods for conservation laws.

Full Product Details

Author:   E.F. Toro
Publisher:   Springer Science+Business Media
Imprint:   Kluwer Academic/Plenum Publishers
Edition:   2001 ed.
Dimensions:   Width: 17.80cm , Height: 5.70cm , Length: 25.40cm
Weight:   2.463kg
ISBN:  

9780306466014

ISBN 10:   0306466015
Pages:   1077
Publication Date:   31 December 2001
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

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-dimensionalUpwind 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.

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