Eulerian and Lagrangian modelling of a solitary wave attack on a seawall

The problem of a solitary wave attack on a vertical seawall is investigated by applying two approaches. The first is a semi-analytical method in which the Euler equations of motion are solved under the assumption of a potential flow by employing an approach based on the fast Fourier transform technique and a numerical time-stepping scheme. The second approach employed to analyse the problem considered is the smoothed particle hydrodynamics (SPH) method, in which the equations are solved in the Lagrangian coordinates. The two methods are used to simulate solitary wave propagation in water of uniform depth, followed by a wave impact on a vertical wall. The simulations focus on the determination of the maximum run-up of the wave on the wall, the calculation of pressures exerted by water on the structure, and the evaluation of water velocities in the vicinity of the structure. The predictions of the two approaches are compared to identify wave regimes for which both methods give satisfactory results. The results of numerical simulations have shown that both proposed methods predict practically the same free-surface profiles for waves of small and moderate amplitudes. For higher waves, some discrepancies between the results of the two methods occur. The two models results have been also compared with empirical data known from the literature, showing good agreement with experimental measurements in terms of the maximum wave run-up and the wave crest residence time at a wall.