31° Convegno Nazionale di Idraulica e Costruzioni Idrauliche Perugia, 9-12 settembre 2008 AN ANALYSI S OF SPH SMOOTHI NG FUNCTI ON MODELLI NG A REGULAR BREAKI NG WAVE D. De Padova 1 , R. A. Dalrymple 2 , M. Mossa 1 , A. F. Petrillo 3 (1) Environmental Engineering and Sustainable Development Department, Technical University of Bari, Via E. Orabona, 4 – 70125 Bari, Italy, e-mail: d.depadova@poliba.it, m.mossa@poliba.it (2) Department of Civil Engineering, Johns Hopkins University, 3400N Charles Street, Baltimore, MD 21218, USA, e-mail: rad@jhu.edu (3) Water Engineering and Chemistry Department, Technical University of Bari, Via E. Orabona, 4 – 70125 Bari, Italy, e-mail: petrillo@poliba.it ABSTRACT The Smooothed Particle Hydrodynamics is a Lagrangian mesh-free particle model introduced by Gingold and Monaghan (1977). In this paper, the SPH Kernel is analyzed in order to find measures of merit for two-dimensional SPH. The smoothing function plays a very important role in the SPH approximations, as it determines the accuracy of the function representation and the efficiency of the computation. The generalized approach in constructing the smoothing functions for the SPH method uses an integral form of function representation with the support of the Taylor series expansion. In addition to theory, comparisons with physical model runs are analyzed, demonstrating the important role of the smoothing function in terms of computational accuracy. The SPH model is applied to the modelling of water waves generated in the wave flume of the Water Engineering and Chemistry Department laboratory of Bari Technical University (Italy). It is shown that the final version is able to model the propagation of regular and breaking waves. 1 I NTRODUCTI ON The numerical technique (SPH) is a gridless, pure Lagrangian method for solving the equations of fluid dynamics. In this paper we analyze the key element in the Smoothed Particle Hydrodynamics (SPH) method, the SPH Kernel, in order to develop a measure of merit for evaluating Kernels in two dimensional SPH. The main features of the SPH method, which is based on integral interpolations, were described in detail by Monaghan (1982), Benz (1990), Monaghan (1992) and Liu (2003). The alternative view is that the fluid domain is represented by nodal points that are scattered in space with no definable grid structure and move with the fluid. Each of these nodal points carry scalar information, density, pressure, velocity components and