Finite Volumes For Complex Applications Iii
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Finite Volumes for Complex Applications III
Author: Raphaèle Herbin
language: en
Publisher: Elsevier Science & Technology
Release Date: 2002
Scientific computing, which involves the analysis of complex systems in real applications with numerical simulations, is becoming an important field of research in itself, in relation to theoretical investigations and physical experiments. In many cases, the underlying mathematical models consist of large systems of partial differential equations, which have to be solved with high accuracy and efficiency. Among the successful methods, in particular for discretizations on unstructured grids, are the Finite Volume schemes. This publication contains the contributions presented at the third Symposium on Finite Volumes for Complex Applications, held in Porquerolles in June 2002. After a critical review of the submitted papers, 96 papers by authors from more than 20 countries are presented in this volume. The subject of these papers ranges from theoretical and numerical results such as theoretical foundation and validation, adaptivity in space and time, higher order discretization and parallelization, to physical,applications, such as multiphase flow and flows through porous media, magnetohydrodynamics, reacting and turbulent flows, elastic structures, granular avalanches, and image processing.
Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems
This volume comprises the first part of the proceedings of the 10th International Conference on Finite Volumes for Complex Applications, FVCA, held in Strasbourg, France, during October 30 to November 3, 2023. The Finite Volume method, and several of its variants, is a spatial discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods are also built to preserve some properties of the continuous equations, including maximum principles, dissipativity, monotone decay of the free energy, asymptotic stability, or stationary solutions. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. In recent years, the efficient implementation of these methods in numerical software packages, more specifically to be used in supercomputers, has drawn some attention. This volume contains all invited papers, as well as the contributed papers focusing on finite volume schemes for elliptic and parabolic problems. They include structure-preserving schemes, convergence proofs, and error estimates for problems governed by elliptic and parabolic partial differential equations. The second volume is focused on finite volume methods for hyperbolic and related problems, such as methods compatible with the low Mach number limit or able to exactly preserve steady solutions, the development and analysis of high order methods, or the discretization of kinetic equations.
Finite Volumes for Complex Applications IV
This volume contains contributions from speakers at the 4th International Symposium on Finite Volumes for Complex Applications, held in Marrakech, Morocco, in July 2005. The subject of these papers ranges from theoretical and numerical results to physical applications. Topics covered include: Theoretical and numerical results • theoretical foundation • convergence • new finite volume schemes • adaptivity • higher order discretization and parallelization Physical applications • multiphase flow and flows through porous media • turbulent flows • shallow water problems • stiff source terms • cryogenic applications • medical and biological applications • image processing Papers on Industrial codes, as well as interdisciplinary approaches are also included in these proceedings.