INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2010; 84:610–630 Published online 23 April 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.2911 A Lagrangian finite element approach for the analysis of fluid–structure interaction problems M. Cremonesi ∗, † , A. Frangi and U. Perego Department of Structural Engineering, Politecnico of Milano, P.za Leonardo da Vinci 32, 20133 Milan, Italy SUMMARY A Lagrangian finite element method for the analysis of incompressible Newtonian fluid flows, based on a continuous re-triangulation of the domain in the spirit of the so-called Particle Finite Element Method, is here revisited and applied to the analysis of the fluid phase in fluid–structure interaction problems. A new approach for the tracking of the interfaces between fluids and structures is proposed. Special attention is devoted to the mass conservation problem. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation fluid–structure interaction problems with evolving free surfaces and breaking waves. The method is validated against the available analytical and numerical benchmarks. Copyright 2010 John Wiley & Sons, Ltd. Received 16 April 2009; Revised 6 October 2009; Accepted 13 March 2010 KEY WORDS: particle methods; Lagrangian approaches; fluid–structure interaction 1. INTRODUCTION The analysis of fluid–structure interaction problems, in which the structure undergoes large defor- mations and the fluid motion is characterized by free surfaces and breaking waves, is of great relevance in many areas of engineering. Generally, the equations of motion for a Newtonian fluid are presented in Eulerian form; this formulation allows to conveniently solve many situations with a fixed domain or control volume. Otherwise, the Arbitrary Lagrangian Eulerian method (ALE) [1], in which the movement of the fluid particles is separated from that of the mesh nodes, is often applied. Typical difficulties of free-surface flow or fluid–structure interaction problems using Eulerian or ALE formulations are the treatment of the convective terms, the modeling of the wave splashing and the tracking of the free-surfaces and of the interfaces between fluids and structures which require dedicated algorithms, such as the Volume of Fluid [2] or the Level Set [3] methods. ∗ Correspondence to: M. Cremonesi, Department of Structural Engineering, Politecnico of Milano, P.za Leonardo da Vinci 32, 20133 Milan, Italy. † E-mail: cremonesi@stru.polimi.it Contract/grant sponsor: Tetra Pak Packaging Solutions S.p.a. Copyright 2010 John Wiley & Sons, Ltd.