Méthodes de caractéristiques pour des systèmes de lois de conservation PDF Download

Author: Setti Ayad
Publisher:
ISBN:
Category :
Languages : fr
Pages :

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Author: Setti Ayad
Publisher: Editions Universitaires Europeennes
ISBN: 9783841788559
Category :
Languages : de
Pages : 124

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Les lois de conservation dont il est question dans cet ouvrage sont celles de la physique ou de la mecanique, lorsque l'etat du systeme considere est un champ. Des methodes de caracteristiques sont developpees pour le probleme de Cauchy associe a un systeme de lois de conservation hyperbolique monodimensionnel et une donnee initiale de variation totale petite. Une transformation (du type Euler-Lagrange) de l'espace (x, t) permet le decouplage des champs caracteristiques au niveau de la vitesse. Elle controle l'evolution de la vitesse et de l'amplitude des ondes et donne une estimation de la decroissance des ondes d'expansion dans une solution admissible du probleme de Cauchy. Une etude complete de cette transformation est effectuee dans le cadre du schema "wave front tracking." Les methodes introduites dans cet ouvrage tentent de lever la difficulte liee a la resolution du probleme de Cauchy ou du probleme mixte tant du point de vue theorique que celui de l'analyse numerique.

Author: LEVEQUE
Publisher: Birkhäuser
ISBN: 3034851162
Category : Science
Languages : en
Pages : 221

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These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.

Author: Randall J. LeVeque
Publisher: Birkhauser
ISBN:
Category : Conservation laws (Mathematics)
Languages : en
Pages : 246

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Author: Amina Sahel
Publisher:
ISBN:
Category :
Languages : fr
Pages : 222

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LE TRAVAIL PRESENTE DANS CETTE THESE EST RELATIF A DES SYSTEMES DE LOIS DE CONSERVATION APPARTENANT A LA CLASSE DE TEMPLE. DE TELS SYSTEMES MODELISENT CERTAINES PHENOMENES CHIMIQUES ET PHYSIQUES. LES SYSTEMES APPARTENANT A LA CLASSE DE TEMPLE POSSEDENT DES PROPRIETES GENERALISANT FIDELEMENT CELLES D'UNE EQUATION SCALAIRE. AINSI, LE BUT DE CE TRAVAIL EST D'ETENDRE UN CERTAIN NOMBRE DE RESULTATS PROUVES DANS LE CAS D'UNE SEULE LOI. ON DEMONTRE D'ABORD DES FORMULES D'INTEGRATION GENERALISANT LA METHODE DES CARACTERISTIQUES. UNE PREUVE DE L'INEGALITE E-D'OLEINIK EST AUSSI PRESENTEE. DE MANIERE PRECISE, ON ETABLIT L'ESTIMATION D'ENTROPIE RELATIVE AU GRADIENT D'UN I-INVARIANT DE RIEMANN (1 I N): C#I > O T.Q. T > O, W#I(U(Y,T)) - W#I(U(X,T))/Y - X C#I/T, P.P. EN (X, Y), X Y UNE DERNIERE PARTIE CONCERNE DES METHODES DE RESOLUTION NUMERIQUE POUR LES SYSTEMES DE TEMPLE. LES SCHEMAS PROPOSES NE NECESSITENT PAS LA RESOLUTION DE PROBLEMES DE RIEMANN

Author: Bruno Després
Publisher: Springer Science & Business Media
ISBN: 3642116574
Category : Mathematics
Languages : fr
Pages : 291

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Les systèmes de lois de conservation non linéaires modélisent les écoulements compressibles et incompressibles dans des domaines extrêmement variés tels que l'aéronautique, l'hydrodynamique, la physique des plasmas, la combustion, le trafic routier, l'élasticité non linéaire. Le cadre mathématique général est celui des systèmes de lois de conservation. Les exemples physiques sont nombreux et souvent spectaculaires. Cela contribue à fonder une nouvelle discipline, la Mécanique des Fluides Numérique. La présentation proposée porte l'accent sur les systèmes que l'on appellera lagrangiens ou écrits en coordonnées de Lagrange, sur leurs relations avec les systèmes en coordonnées d'Euler et sur les possibilités que cela offre pour la construction et l'analyse de schémas numériques entropiques. De nombreux exemples numériques sont présentés en liaison avec le contexte physique, ainsi que des exercices. It has long been observed that systems of conservation laws written in the Lagrange variable offer a good alternative for the numerical computation of approximate solutions. In this monograph we seek to develop a systematic presentation of the use of the Lagrange variable for the analysis and discretization of systems of conservation laws arising in continuum mechanics.

Author: P. L. Roe
Publisher: World Scientific
ISBN: 9810248105
Category : Mathematics
Languages : en
Pages : 418

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Book Description
This book consists of 20 review articles dedicated to Prof. Philip Roe on the occasion of his 60th birthday and in appreciation of his original contributions to computational fluid dynamics. The articles, written by leading researchers in the field, cover many topics, including theory and applications, algorithm developments and modern computational techniques for industry.

Author: Tatsien Li
Publisher: World Scientific
ISBN: 9814546429
Category :
Languages : en
Pages : 286

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This volume contains 30 research papers presenting the recent development and trend on the following subjects: nonlinear hyperbolic equations (systems); nonlinear parabolic equations (systems); infinite-dimensional dynamical systems; applications (free boundary problems, phase transitions, etc.).

Author: Robert Klöfkorn
Publisher: Springer Nature
ISBN: 3030436519
Category : Computers
Languages : en
Pages : 727

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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: María Luz Muñoz-Ruiz
Publisher: Springer Nature
ISBN: 3030728501
Category : Mathematics
Languages : en
Pages : 269

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The present volume contains selected papers issued from the sixth edition of the International Conference "Numerical methods for hyperbolic problems" that took place in 2019 in Málaga (Spain). NumHyp conferences, which began in 2009, focus on recent developments and new directions in the field of numerical methods for hyperbolic partial differential equations (PDEs) and their applications. The 11 chapters of the book cover several state-of-the-art numerical techniques and applications, including the design of numerical methods with good properties (well-balanced, asymptotic-preserving, high-order accurate, domain invariant preserving, uncertainty quantification, etc.), applications to models issued from different fields (Euler equations of gas dynamics, Navier-Stokes equations, multilayer shallow-water systems, ideal magnetohydrodynamics or fluid models to simulate multiphase flow, sediment transport, turbulent deflagrations, etc.), and the development of new nonlinear dispersive shallow-water models. The volume is addressed to PhD students and researchers in Applied Mathematics, Fluid Mechanics, or Engineering whose investigation focuses on or uses numerical methods for hyperbolic systems. It may also be a useful tool for practitioners who look for state-of-the-art methods for flow simulation.