Modelling and simulation of the sea-landing of aerial vehicles using the Particle Finite Element Method P. Ryzhakov a,n , R. Rossi a , A. Viña b , E. Oñate a a Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Spain b CIMSA Ingenieria de Sistemas, Spain article info Article history: Received 22 October 2012 Accepted 30 March 2013 Available online 10 May 2013 Keywords: Fluid–structure interaction Water landing UAV PFEM Wedge impact Incompressible flows abstract In this paper the Particle Finite Element Method (PFEM) is applied to the simulation of the sea-landing of an unmanned aerial vehicle (UAV). The problem of interest consists in modelling the impact of the vehicle against the water surface, analyzing the main kinematic and dynamic quantities (such as loads exerted upon the capsule at the moment of the impact). The PFEM, a methodology well-suited for free- surface flow simulation is used for modelling the water while a rigid body model is chosen for the vehicle. The vehicle under consideration is characterized by low weight. This leads to difficulties in modelling the fluid–structure interaction using standard Dirichlet–Neumann coupling. We apply a modified partitioned strategy introducing the interface Laplacian into the pressure Poisson's equation for obtaining a convergent FSI solution. The paper concludes with an industrial example of a vehicle sea- landing modelled using PFEM. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction and outline The sea-landing of aerial vehicles is one important practical application where numerical simulation of fluid–structure inter- action (FSI) is of great importance since the preliminary physical tests turn out to be excessively expensive. The simulation tests can provide both qualitative and quantitative insight into the move- ment of the vehicle and predict the impact forces. It is worth mentioning that up-to-date there exists a rather sparse literature on the sea-landing studies. Experimental inves- tigations of the water landing were presented in Vaughan (1959). Numerical studies can be found e.g. in Littell (2007) where the commercial software LS-DYNA was used. However, several of the existing fluid–structure interaction techniques can be applied to the problem of interest. One such possibility is the Arbitrary Lagrangian Eulerian (ALE) approach known for its accuracy (see e.g. Donea et al., 1982 or Souli et al., 2000). Unfortunately, even the most advanced ALE formulations arrive to their limits when the domain shape deformations are large, which is the case for the problem at hand. In such situations, re-meshing becomes inevi- table. Another alternative are the fixed grid approaches equipped with the volume of fluid (VOF) or the Level set method (Legay et al., 2006; Rossi et al., 2013). Although possible, the use of fixed grid methods is not trivial for the problem at hand, since it would require dealing with an FSI boundary cutting the grid elements at arbitrary positions. This would require implementing some sort of embedded technique (Codina et al., 2009; Ryzhakov and Oñate, 2010). Smooth Particle Hydrodynamics (SPH)-based approaches (see e.g. Liu, 2003; Antoci et al., 2007) represent a viable alter- native and we verify our formulation against one of the few available benchmark examples (Oger et al., 2006). The problem of the majority of SPH methods is related to the artificial compressibility they usually introduce, which leads to the genera- tion and propagation of non-physical pressure waves in the fluid domain. Such effects may be relevant when estimating the impact forces. Yet another possibility relies on applying the Particle Finite Element Method (PFEM) (Oñate et al., 2004; Idelsohn et al., 2004; Larese et al., 2008; Ryzhakov et al., 2010). PFEM is a class of Lagrangian Finite Element methods developed for treating free- surface flows and it enables efficient treatment of such complex FSI problems. This option is explored here. We present an approach where the PFEM fluid formulation is coupled to the rigid body model representing the vehicle. The rigid body approx- imation is a reasonable choice considering that the deformations of the solid are of no interest in the study. In the present study the unmanned aerial vehicle (UAV) under consideration is characterized by a low weight. The average density, when empty, is some three times lower than that of water. In such case standard Dirichlet–Neumann FSI strategies require excessive number of coupling iterations or do not converge Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.oceaneng.2013.03.015 n Corresponding author. Tel.: +34 934017399. E-mail address: pryzhakov@cimne.upc.edu (P. Ryzhakov). URLS: http://www.cimne.com (P. Ryzhakov), http://www.cimsa.com (A. Viña). Ocean Engineering 66 (2013) 92–100