EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Free access article

Issue ESAIM: PROC
Volume 18, 2007
Paris-sud working group on modelling and scientific computing 2006-2007
Page(s) 120 - 132
DOI 10.1051/proc:071810
Published online 12 September 2007

ESAIM: Proc., 2007, Vol. 18, pp. 120-132
DOI: 10.1051/proc:071810

Fluid-Particle simulations with FreeFem++

Aline Lefebvre

Laboratoire de Mathématiques, Université Paris-Sud, Orsay, France;

Aline.Lefebvre@math.u-psud.fr

(Published online: 12 September 2007)

Abstract
We present here a method to simulate the motion of rigid particles in a Newtonian fluid. The rigid motion is enforced by penalizing the strain tensor on the rigid domain and the time discretization is performed using the method of characteristics. This leads to a generalized Stokes variational formulation on the whole domain which can easily be implemented from any Finite Element Stokes/Navier-Stokes solver. In order to ensure robustness, we describe a strategy to take collisions into account. To validate the method, simulations implemented with FreeFem++ are presented.


Résumé
Nous présentons ici une méthode pour simuler des écoulements de particules rigides dans un fluide Newtonien. Le mouvement rigide est imposé grâce à une pénalisation du tenseur des déformations sur le domaine rigide et la discrétisation en temps est effectuée en utilisant la méthode des caractéristiques. Cela nous permet d'obtenir une formulation variationnelle sur le domaine tout entier de type Stokes généralisé qui peut être programmée facilement à partir de tout solveur éléments finis pour Stokes/Navier-Stokes. Afin d'assurer la robustesse du code, on décrit une stratégie pour prendre en compte les collisions. Pour valider la méthode, on présente des simulations implémentées sous FreeFem++.


Mathematics Subject Classification. 76M10, 76T20, 76D05, 65M60

Key words: particulate flows, fluid-particle flows, direct numerical simulation, penalty method, Navier-Stokes equations, finite-element method, inelastic contacts


© EDP Sciences, ESAIM 2007


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.