ESAIM: PROCEEDINGS, August 2008, Vol. 24, p. 1-13 C. Dobrzynski, P. Frey, Ph. Pebay, Editors A CELL-CENTERED ARBITRARY LAGRANGIAN EULERIAN (ALE) METHOD FOR MULTI-MATERIAL COMPRESSIBLE FLOWS P.-H. Maire 1 , M. De Buhan 2 , A. Diaz 3 , C. Dobrzynski 4 , G. Kluth 5 and F. Lagouti` ere 6 Abstract. We present an original and accurate unstructured cell-centered ALE algorithm devoted to the simulation of two-dimensional multi-material compressible fluid flows. Gas dynamics equations are discretized with an unstructured finite volume scheme. R´ esum´ e. Nous pr´ esentons dans cet article une m´ ethode du type ALE appliqu´ ee`alar´ esolution d’´ ecoulements multimat´ eriaux compressibles. Les ´ equations de la dynamique des gaz sont discr´ etis´ ees sur des maillages non structur´ es en utilisant un sch´ ema du type volume fini. Introduction Fidelity in tracking multifluid interfaces makes the Lagrangian frame of reference attractive for a wide variety of hydrocode applications. Unfortunately, since the mesh moves with the flow, convolution of the flow can lead to mesh deformation and tangling. The Arbitrary Lagrangian-Eulerian (ALE) framework, introduced by [5], allows a computation to be broken up into a Lagrangian phase, a mesh rezoning phase intended to correct for mesh deformation, and a remapping phase where computed physical values are advanced to the rezoned mesh. The Arbitrary Lagrangian-Eulerian framework has demonstrated the ability to simultaneously elicit the advantages of both the Lagrangian and Eulerian frames of reference. The goal of this paper is to describe an original cell-centered ALE strategy for multi-material fluid flows and to focus more precisely on the description of the rezoning phase. Classically, Lagrangian step uses a staggered scheme, in which velocities are vertex- centered and the other variables are cell-centered [3]. The main difficulty with this approach lies in the fact that one needs special treatment for momentum remapping [9]. As our Lagrangian step is fully cell-centered [11,12], we avoid such special treatment. Our rezoning step utilizes the “local” minimization of nodally based objectives functions [6]. The remapping step is based on an unstructured extension of the “simplified face-based donor- cell” method of [14]. The remainder of this paper is organized as follows. We first describe the different steps of the ALE formulation. Then, computational results are given to assess the robustness and the accuracy of this method. 1 UMR CELIA, Universit´ e Bordeaux I, 351 Cours de la Lib´ eration, 33 405 Talence, France. 2 UPMC, Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France. 3 Department of Mathematics and Computer Science, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053-0290, USA 4 UMR 5251, IMB, Universit´ e Bordeaux I et INRIA Bordeaux - Sud-Ouest, 351 Cours de la Lib´ eration, 33 405 Talence, France. 5 CEA-DIF/DSSI, BP 12 91680 Bruy` eres Le Chˆatel, France. 6 Universit´ e Paris-Diderot (Paris 7) and Laboratoire Jacques-Louis Lions (CNRS UMR 7598), 175, rue du Chevaleret, 75013 Paris, France. c  EDP Sciences, SMAI 2008 Article published by EDP Sciences and available at http://www.edpsciences.org/proc or http://dx.doi.org/10.1051/proc:2008026