A CRITICAL INVESTIGATION OF SPH APPLIED TO PROBLEMS WITH FREE SURFACES 1 A critical investigation of Smoothed Particle Hydrodynamics applied to problems with free surfaces D. Le Touzé 2 , A. Colagrossi 1, 3, ∗ G. Colicchio 1, 3 and M. Greco 1, 3 1 CNR-INSEAN, The Italian Ship Model Basin, via di Vallerano 139, 00128 Roma - Italy 2 LUNAM Université, École Centrale de Nantes, LHEEA Lab. (UMR CNRS), Nantes - France 3 CeSOS/CAMOS, Center for Ship and Ocean Structures, Dept. of Marine Technology, NTNU, Trondheim - Norway SUMMARY In this paper, an in-depth study of SPH method, in its original weakly compressible version, is achieved on dedicated two- and three-dimensional free-surface flow test cases. These rather critical prototype problems shall constitute suitable test cases to get through when building a free-surface SPH model. The present work aims at investigating various numerical aspects of this method, often little mentioned in literature. In particular, a great care is paid to the dynamic part of the solution, which is critical to the local hydrodynamic load prediction. The role of numerical errors in the development of acoustic frequencies in the pressure signals is discussed, as well as the influence of the choice of the sound velocity. On the shown test problems, it is also evidenced that some numerical tools are crucial to ensure the robustness and accuracy of the standard SPH method. The convergence of our model is heuristically proved on these nonlinear prototype tests, showing at the same time the very satisfactory level of accuracy reached. Through these tests, some other numerical specificities of the SPH method are discussed, such as the self-redistribution of the particles occurring during the Lagrangian evolution. A higher-order model is also proposed, and its advantages and drawbacks are discussed. Copyright c  2013 John Wiley & Sons, Ltd. Received . . . KEY WORDS: Smoothed Particle Hydrodynamics; SPH validation test cases; Free surface flows; Convergence tests; SPH pressure evaluation; Weak-compressibility; Higher-order SPH formulation. 1. INTRODUCTION In the last two decades, a new class of numerical solvers, based on the use of meshless scattered sets of nodes, has started to be successfully applied to various physical problems. In the case of complex problems dominated by convection phenomena and characterized by the presence of deformable interfaces, the discretization methods commonly applied, such as finite-difference, finite-element or finite-volume methods, can have difficulties to find efficient solutions, and dedicated numerical techniques are required. Such problems could be effectively solved by particle methods, such as the Smoothed Particle Hydrodynamics (SPH) first proposed in [1] and [2]. * Correspondence to: CNR-INSEAN, via di Vallerano 139, 00128 Roma - Italy. E-mail: a.colagrossi@insean.it Copyright c  2013 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids (2013) Prepared using fldauth.cls DOI: 10.1002/fld