Finite Volumes For Complex Applications Vi Problems Perspectives

Author : Jaroslav Fořt,Jiří Fürst,Jan Halama,Raphaèle Herbin,Florence Hubert
Publisher : Springer Science & Business Media
Page : 1003 pages
File Size : 40,5 Mb
Release : 2011-07-21
Category : Mathematics
ISBN : 9783642206719

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Finite Volumes for Complex Applications VI Problems & Perspectives by Jaroslav Fořt,Jiří Fürst,Jan Halama,Raphaèle Herbin,Florence Hubert Pdf

Finite volume methods are used for various applications in fluid dynamics, magnetohydrodynamics, structural analysis or nuclear physics. A closer look reveals many interesting phenomena and mathematical or numerical difficulties, such as true error analysis and adaptivity, modelling of multi-phase phenomena or fitting problems, stiff terms in convection/diffusion equations and sources. To overcome existing problems and to find solution methods for future applications requires many efforts and always new developments. The goal of The International Symposium on Finite Volumes for Complex Applications VI is to bring together mathematicians, physicists and engineers dealing with Finite Volume Techniques in a wide context. This book, divided in two volumes, brings a critical look at the subject (new ideas, limits or drawbacks of methods, theoretical as well as applied topics).

Author : Roland Vilsmeier,Fayssal Benkhaldoun,Dieter Hänel
Publisher : Hermes Science Publications
Page : 889 pages
File Size : 53,6 Mb
Release : 1999
Category : Technology & Engineering
ISBN : 2746200570

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Finite Volumes for Complex Applications by Roland Vilsmeier,Fayssal Benkhaldoun,Dieter Hänel Pdf

Finite Volume methods are methods directly related to the numerical solution of conservation laws. Systems of such conservation laws govern wide fields of physics and the efficiency of corresponding solution methods is an essential requirement from basic research and industry. Since the efficiency of any method must be measured by the quality of the result compared to the computational cost to spend for, corresponding developments are widely spread, ranging from very fundamental numerical analysis up to the efficient use of modern computer hardware. Although in the past the numerical methodology has made large progresses, many problems and difficulties remain, requiring further intensive research. The present proceedings summarise the contributions to be presented at the second international symposium on Finite Volumes for Complex Applications - Problems and Perspectives. The first symposium of this series was held summer 1996 at INSA de Rouen in France. Based on the success of this first conference, the symposium in Duisburg has again received an unexpected high attention in the numeric community. After a critical review of the submitted contributions, 98 papers by authors from 20 countries are presented in this volume. In a rough estimation, about half of the contributions can be assigned to analysis and numerics of different methods whereas the other half is essentially concerned with application and computational aspects of methods.

Author : Fayssal Benkhaldoun
Publisher : Kogan Page Limited
Page : 738 pages
File Size : 53,7 Mb
Release : 1996
Category : Technology & Engineering
ISBN : 2866015568

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Finite Volumes for Complex Applications by Fayssal Benkhaldoun Pdf

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. The first symposium of the series was held in Rouen in 1996.

Author : Emmanuel Franck,Jürgen Fuhrmann,Victor Michel-Dansac,Laurent Navoret
Publisher : Springer Nature
Page : 381 pages
File Size : 51,5 Mb
Release : 2023-11-01
Category : Mathematics
ISBN : 9783031408649

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Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems by Emmanuel Franck,Jürgen Fuhrmann,Victor Michel-Dansac,Laurent Navoret Pdf

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.

Author : Jürgen Fuhrmann,Mario Ohlberger,Christian Rohde
Publisher : Springer
Page : 518 pages
File Size : 41,5 Mb
Release : 2014-05-16
Category : Mathematics
ISBN : 9783319055916

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Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems by Jürgen Fuhrmann,Mario Ohlberger,Christian Rohde Pdf

The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space 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 preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. 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. Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations.

Author : Clément Cancès,Pascal Omnes
Publisher : Springer
Page : 559 pages
File Size : 52,7 Mb
Release : 2017-05-22
Category : Mathematics
ISBN : 9783319573946

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Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems by Clément Cancès,Pascal Omnes Pdf

This book is the second volume of proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017). It includes reviewed contributions reporting successful applications in the fields of fluid dynamics, computational geosciences, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. 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 l evel. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is useful for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as for engineers working in numerical modeling and simulations.

Author : Jürgen Fuhrmann,Mario Ohlberger,Christian Rohde
Publisher : Springer
Page : 450 pages
File Size : 40,8 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9783319056845

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects by Jürgen Fuhrmann,Mario Ohlberger,Christian Rohde Pdf

The first volume of the proceedings of the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) covers topics that include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers, as well as the reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods. Altogether, a rather comprehensive overview is given of the state of the art in the field. The finite volume method in its various forms is a space 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 preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. 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. Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations.

Author : Clément Cancès,Pascal Omnes
Publisher : Springer
Page : 476 pages
File Size : 46,7 Mb
Release : 2017-05-23
Category : Mathematics
ISBN : 9783319573977

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Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects by Clément Cancès,Pascal Omnes Pdf

This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier–Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asy mptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. 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. The book is a valuable resource for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.

Author : Robert Klöfkorn,Eirik Keilegavlen,Florin A. Radu,Jürgen Fuhrmann
Publisher : Springer Nature
Page : 727 pages
File Size : 41,6 Mb
Release : 2020-06-09
Category : Computers
ISBN : 9783030436513

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Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples by Robert Klöfkorn,Eirik Keilegavlen,Florin A. Radu,Jürgen Fuhrmann Pdf

The proceedings of the 9th conference on "Finite Volumes for Complex Applications" (Bergen, June 2020) are structured in two volumes. The first volume collects the focused invited papers, as well as the reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods. Topics covered include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. Altogether, a rather comprehensive overview is given on the state of the art in the field. The properties of the methods considered in the conference give them distinguished advantages for a number of applications. These include fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory, carbon capture utilization and storage, geothermal energy and further topics. The second volume covers reviewed contributions reporting successful applications of finite volume and related methods in these fields. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability, making the finite volume methods 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. The book is a valuable resource for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.

Author : Raphaèle Herbin,Dietmar Kröner
Publisher : Elsevier Science & Technology
Page : 860 pages
File Size : 50,7 Mb
Release : 2002
Category : Mathematics
ISBN : UOM:39015063199536

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Finite Volumes for Complex Applications III by Raphaèle Herbin,Dietmar Kröner Pdf

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.

Author : Jérôme Droniou,Robert Eymard,Thierry Gallouët,Cindy Guichard,Raphaèle Herbin
Publisher : Springer
Page : 497 pages
File Size : 45,7 Mb
Release : 2018-07-31
Category : Mathematics
ISBN : 9783319790428

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The Gradient Discretisation Method by Jérôme Droniou,Robert Eymard,Thierry Gallouët,Cindy Guichard,Raphaèle Herbin Pdf

This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.span style="" ms="" mincho";mso-bidi-font-family:="" the="" core="" properties="" and="" analytical="" tools="" required="" to="" work="" within="" gdm="" are="" stressed,="" it="" is="" shown="" that="" scheme="" convergence="" can="" often="" be="" established="" by="" verifying="" a="" small="" number="" of="" properties.="" scope="" some="" featured="" techniques="" results,="" such="" as="" time-space="" compactness="" theorems="" (discrete="" aubin–simon,="" discontinuous="" ascoli–arzela),="" goes="" beyond="" gdm,="" making="" them="" potentially="" applicable="" numerical="" schemes="" not="" (yet)="" known="" fit="" into="" this="" framework.span style="font-family:" ms="" mincho";mso-bidi-font-family:="" this="" monograph="" is="" intended="" for="" graduate="" students,="" researchers="" and="" experts="" in="" the="" field="" of="" numerical="" analysis="" partial="" differential="" equations./ppiiiiibr/i/i/i/i/i/p

Author : Carlos Parés
Publisher : Springer Nature
Page : 463 pages
File Size : 45,5 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9783031552649

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Hyperbolic Problems: Theory, Numerics, Applications. Volume II by Carlos Parés Pdf

Author : Grazia Lamanna,Simona Tonini,Gianpietro Elvio Cossali,Bernhard Weigand
Publisher : Springer Nature
Page : 311 pages
File Size : 43,5 Mb
Release : 2020-03-14
Category : Technology & Engineering
ISBN : 9783030333386

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Droplet Interactions and Spray Processes by Grazia Lamanna,Simona Tonini,Gianpietro Elvio Cossali,Bernhard Weigand Pdf

This book provides a selection of contributions to the DIPSI workshop 2019 (Droplet Impact Phenomena & Spray Investigations) as well as recent progress of the Int. Research Training Group “DROPIT”.The DIPSI workshop, which is now at its thirteenth edition, represents an important opportunity to share recent knowledge on droplets and sprays in a variety of research fields and industrial applications. The research training group “DROPIT” is focused on droplet interaction technologies where microscopic effects influence strongly macroscopic behavior. This requires the inclusion of interface kinetics and/or a detailed analysis of surface microstructures. Normally, complicated technical processes cover the underlying basic mechanisms, and therefore, progress in the overall process modelling can hardly be gained. Therefore, DROPIT focuses on the underlying basic processes. This is done by investigating different spatial and/or temporal scales of the problems and by linking them through a multi-scale approach. In addition, multi-physics are required to understand e.g. problems for droplet-wall interactions, where porous structures are involved.

Author : Gayaz Khakimzyanov,Denys Dutykh,Zinaida Fedotova,Oleg Gusev
Publisher : Springer Nature
Page : 296 pages
File Size : 46,9 Mb
Release : 2020-09-15
Category : Mathematics
ISBN : 9783030462673

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Dispersive Shallow Water Waves by Gayaz Khakimzyanov,Denys Dutykh,Zinaida Fedotova,Oleg Gusev Pdf

This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves. Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and applications. From modelling tsunami waves to smaller scale coastal processes, this book will be an indispensable resource for those looking to be brought up-to-date in this active area of scientific research. Beginning with an introduction to various dispersive long wave models on the flat space, the authors establish a foundation on which readers can confidently approach more advanced mathematical models and numerical techniques. The first two chapters of the book cover modelling and numerical simulation over globally flat spaces, including adaptive moving grid methods along with the operator splitting approach, which was historically proposed at the Institute of Computational Technologies at Novosibirsk. Later chapters build on this to explore high-end mathematical modelling of the fluid flow over deformed and rotating spheres using the operator splitting approach. The appendices that follow further elaborate by providing valuable insight into long wave models based on the potential flow assumption, and modified intermediate weakly nonlinear weakly dispersive equations. Dispersive Shallow Water Waves will be a valuable resource for researchers studying theoretical or applied oceanography, nonlinear waves as well as those more broadly interested in free surface flow dynamics.

Author : Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia
Publisher : Springer
Page : 312 pages
File Size : 42,6 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9783319946764

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Numerical Methods for PDEs by Daniele Antonio Di Pietro,Alexandre Ern,Luca Formaggia Pdf

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.