Propagation of gravity wave-packets through a Delta-SPH method

In the present work we study the capability of the diffusive weakly-compressible SPH scheme described in Antuono et al. [1] (hereinafter denoted as Delta-SPH) to reproduce the propagation of 2D gravity waves generated by a wavemaker into a 2D wave basin. In the first part we consider regular waves with height-to-depth ratios spreading to deep to shallow water and steepness values chosen to emphasize nonlinear behavior in wave propagation. The results of the Mixed-Eulerian-Lagrangian Boundary Element Method (hereinafter BEM-MEL) developed in [3] are used for comparison. This comparison allows inspecting the accuracy of the Delta-SPH to approximate inviscid fluids. In the second part we study the propagation of a wave packet. The experimental data of Dommermuth et al. [4] have been considered for validating the capability of the SPH solver to follow the evolution of a wave train towards the focusing. The results clearly show a good match between Delta-SPH, BEM-MEL and experiments. The influence of the weakly-compressibility assumption on the results is inspected and a convergence analysis is provided in order to understand the minimal spatial resolution needed to get a good representation of gravity waves.