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Author: TSUTOMU.. NARUSAWA
Publisher:
ISBN:
Category :
Languages : fr
Pages : 224
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Book Description
CONSIDERATION D'UNE NOUVELLE METHODE DE DISCRETISATION AYANT EU LIEU AVEC LA METHODE DE VOLUME DE CONTROLE. PROPOSITION DE CRITERES DES SCHEMAS DE DECENTRAGE ET DES NOUVEAUX SCHEMAS, SUPPRIMANT COMPLETEMENT LA DIFFUSION NUMERIQUE, POUR UNE EQUATION DE DIFFUSION-CONVECTION A CONVECTION DOMINANTE. PROPOSITION D'UNE NOUVELLE PROCEDURE DE DISCRETISATION POUR UNE EQUATION HYPERBOLIQUE PERMETTANT D'OBTENIR UNE FAMILLE DE SCHEMAS D'ELEMENTS FINIS D'UN ORDRE DE TRONCATURE QUELCONQUE. TESTS NUMERIQUES DE LA PLUPART DES NOUVEAUX SCHEMAS PROPOSES
Author: TSUTOMU.. NARUSAWA
Publisher:
ISBN:
Category :
Languages : fr
Pages : 224
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Book Description
CONSIDERATION D'UNE NOUVELLE METHODE DE DISCRETISATION AYANT EU LIEU AVEC LA METHODE DE VOLUME DE CONTROLE. PROPOSITION DE CRITERES DES SCHEMAS DE DECENTRAGE ET DES NOUVEAUX SCHEMAS, SUPPRIMANT COMPLETEMENT LA DIFFUSION NUMERIQUE, POUR UNE EQUATION DE DIFFUSION-CONVECTION A CONVECTION DOMINANTE. PROPOSITION D'UNE NOUVELLE PROCEDURE DE DISCRETISATION POUR UNE EQUATION HYPERBOLIQUE PERMETTANT D'OBTENIR UNE FAMILLE DE SCHEMAS D'ELEMENTS FINIS D'UN ORDRE DE TRONCATURE QUELCONQUE. TESTS NUMERIQUES DE LA PLUPART DES NOUVEAUX SCHEMAS PROPOSES
Author: Abdeslam Koubaa
Publisher: GRIN Verlag
ISBN: 3346024997
Category : Mathematics
Languages : fr
Pages : 103
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Book Description
Thèse de Master de l’année 2018 dans le domaine Mathématiques - Mathématiques appliquées, note: 17, Mohamed I University (Faculté Pluridisciplinaire Nador), cours: Analyse Numérique, langue: Français, résumé: L'objectif de ce travail est de proposer et d'étudier des schémas numériques de type volumes finis adaptés à la simulation de certains problèmes de convection et de diffusion. La première partie est consacrée àl'étude de la convergence des schémas numériques de type volumes finis. Par la suite, l’auteur analyse trois types de schémas, conservatifs et consistants au sens des volumes finis l'un totalement explicite, le deuxième totalement implicite, puis un nouveau θ- schéma totalement implicite. Après, l’auteur traité et analysé les schémas de type volumes finis explicite, implicite et θ-schéma implicite pour l'équation non linéaire instationnaire mono-dimensionnelle de convection-diffusion, où le terme de convection est approché par un schéma de Godunov décentré amont et le terme de diffusion par une approximation d'ordre 1. Dans la deuxième partie, l’auteur présente la simulation numérique de l'équation de la chaleur, correspondant aux schémas explicite et implicite et Crank-Nicolson, en utilisant langage de programmation matlab pour visualiser les courbes solutions. Les phénomènes de transport, tels que les transferts de chaleur et de masse, jouent un rôle très important dans la vie humaine. Les gaz et les liquides nous entourent, les flux à l'intérieur de notre corps, et ont une influence profonde sur l'environnement dans lequel nous vivons. Lorsqu'il s'agit du phénomène de transport, on distingue généralement deux processus, la convection et la diffusion.
Author: Jean Donea
Publisher: John Wiley & Sons
ISBN: 9780471496663
Category : Science
Languages : en
Pages : 366
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Book Description
Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.
Author: Mostafa Belghit (auteur d'une thèse de sciences.)
Publisher:
ISBN:
Category :
Languages : fr
Pages :
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Book Description
Author: Hans-Görg Roos
Publisher: Springer Science & Business Media
ISBN: 3662032066
Category : Mathematics
Languages : en
Pages : 364
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Book Description
The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
Author: E.L. Ortiz
Publisher: Elsevier
ISBN: 0080872441
Category : Computers
Languages : en
Pages : 447
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Book Description
This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations. There is a balance between theoretical studies of approximation processes, the analysis of specific numerical techniques and the discussion of their application to concrete problems relevant to engineering and science. Special consideration has been given to innovative numerical techniques and to the treatment of three-dimensional and singular problems. These topics are discussed in several of the invited papers.The contributed papers are divided into five parts: techniques of approximation theory which are basic to the numerical treatment of differential equations; numerical techniques based on discrete processes; innovative methods based on polynomial and rational approximation; variational inequalities, conformal transformation and asymptotic techniques; and applications of differential equations to problems in science and engineering.
Author: K.W. Morton
Publisher: CRC Press
ISBN: 1351359673
Category : Mathematics
Languages : en
Pages : 385
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Book Description
Accurate modeling of the interaction between convective and diffusive processes is one of the most common challenges in the numerical approximation of partial differential equations. This is partly due to the fact that numerical algorithms, and the techniques used for their analysis, tend to be very different in the two limiting cases of elliptic and hyperbolic equations. Many different ideas and approaches have been proposed in widely differing contexts to resolve the difficulties of exponential fitting, compact differencing, number upwinding, artificial viscosity, streamline diffusion, Petrov-Galerkin and evolution Galerkin being some examples from the main fields of finite difference and finite element methods. The main aim of this volume is to draw together all these ideas and see how they overlap and differ. The reader is provided with a useful and wide ranging source of algorithmic concepts and techniques of analysis. The material presented has been drawn both from theoretically oriented literature on finite differences, finite volume and finite element methods and also from accounts of practical, large-scale computing, particularly in the field of computational fluid dynamics.
Author: Katherine Mer
Publisher:
ISBN: 9782726110492
Category :
Languages : en
Pages : 144
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Book Description
LE TRAVAIL PRESENTE DANS CETTE THESE EST PRINCIPALEMENT UNE CONTRIBUTION A L'ANALYSE D'APPROXIMATIONS STABILISEES POUR DES PROBLEMES DE CONVECTION-DIFFUSION LINEAIRES. UNE ETUDE NUMERIQUE D'UN PROBLEME D'INTERACTION FLUIDE-STRUCTURE EST EGALEMENT PRESENTEE. POUR UNE EQUATION DE CONVECTION-DIFFUSION STATIONNAIRE, ON ANALYSE LA PRECISION D'UN SCHEMA ELEMENTS FINIS COMPORTANT UN TERME DE STABILISATION SOUS FORME DE DISSIPATION DU QUATRIEME ORDRE. DANS UNE PREMIERE PARTIE, ON SE RESTREINT A UNE ANALYSE POUR DES MAILLAGES SIMPLICIAUX REGULIERS AU SENS DES ELEMENTS FINIS. POUR UN PROBLEME DANS IR#N AVEC N 3, ON OBTIENT DES ESTIMATIONS DE L'ERREUR D'APPROXIMATION DANS L#2 ET DANS H#1 POUR UNE DISSIPATION SOUS FORME VARIATIONNELLE. DANS LE CAS BIDIMENSIONNEL, ON ETUDIE PLUS PARTICULIEREMENT UN SCHEMA DE TYPE JAMESON, COMPOSE D'UNE PARTIE CENTREE DE TYPE MIXTE ELEMENTS FINIS/VOLUMES FINIS ET D'UNE DISSIPATION EN DIFFERENCES QUATRIEMES NON CONSISTANTE. DANS UNE DEUXIEME PARTIE, ON CONSIDERE L'APPROXIMATION D'UN PROBLEME DE CONVECTION-DIFFUSION DONT LA SOLUTION PRESENTE DES COUCHES LIMITES. ON OBTIENT DES ESTIMATIONS D'ERREUR DANS LA NORME DE L'ENERGIE POUR UN SCHEMA ELEMENTS FINIS AVEC UNE DISSIPATION DU QUATRIEME ORDRE CONSISTANTE, POUR DES MAILLAGES TRIANGULAIRES LOCALEMENT ANISOTROPES DANS LES COUCHES LIMITES. LE SCHEMA ETUDIE EST COMPARE A DES SCHEMAS VOLUMES FINIS DU SECOND ORDRE. DANS UNE TROISIEME PARTIE, ON ANALYSE LA CONSISTANCE LOCALE DES SCHEMAS AYANT LA PROPRIETE DE PRESERVATION DE LA LINEARITE, SUR DES MAILLAGES NON STRUCTURES. UNE QUATRIEME PARTIE EST CONSACREE A L'ETUDE NUMERIQUE D'UN SCHEMA IMPLICITE LINEARISE DANS LE CADRE DE L'ANALYSE DU FLOTTEMENT D'UN PROFIL D'AILE DANS UN ECOULEMENT
Author: Dmitri Kuzmin
Publisher: SIAM
ISBN: 1611973600
Category : Science
Languages : en
Pages : 321
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Book Description
This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory.?Finite Element Methods for Computational Fluid Dynamics: A Practical Guide?explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov?Galerkin approximations, Taylor?Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes, and covers Petrov?Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the k-epsilon turbulence model in its presentation of the FEM for incompressible flow problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.?
Author: Howard Elman
Publisher: OUP Oxford
ISBN: 0191667927
Category : Mathematics
Languages : en
Pages : 495
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Book Description
This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.
