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Cours Année : 2016

Introduction to the finite element method applied to incompressible fluid mechanics

Résumé

These lecture notes are intended for undergraduate students. It is expected that the students have already been taught Fluid Mechanics and the Finite Element method. However, a brief review of these two subjects is given in chapters 1 and 3. The main goal of these lecture notes is to present the peculiarities of the finite element method when used for the computation of Newtonian Incompressible flows described by the Navier-Stokes equations. The approach taken here is to give basic knowledge about the generic difficulties one will have to deal with while using a Computational Fluid Dynamics (CFD) code. The presentation will be quite brief on theoretical aspects. Instead, we shall give a lot of practical examples. For a more complete and rigorous approach, the reader is referred for example to Ern and Guermond’s book [EG04] or to the book by Elman et al. [ESW14]. Each difficulty will be examined by considering a model problem, which usually comes from a simplification of the incompressible Navier-Stokes equations. This will help us in bringing up the cause and possible cure of the aforementioned difficulties. At the beginning of each chapter, we frame the terms in the Navier-Stokes equations on which we shall focus our attention. The computer program we use in the examples is the Cast3M finite element code. However any other program using the same method (FreeFEM, Comsol... ) could be used because the difficulties we look at are generic. In order for the student to reproduce and build on the examples, the significant part of the Cast3M data file is given. The complete data files can be found on the Cast M Web site: http://www-cast3m.cea.fr/.
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Dates et versions

hal-04108255 , version 1 (26-05-2023)

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  • HAL Id : hal-04108255 , version 1

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Stephane Gounand, Sergey Kudriakov. Introduction to the finite element method applied to incompressible fluid mechanics. Engineering school. Introduction à la méthode des éléments finis en mécanique des fluides incompressibles, ENSTA ParisTech, France. 2016, pp.132. ⟨hal-04108255⟩
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