Modelling of wave generation in a numerical tank by SPH method

There have been many mathematical and physical modelling strategies to represent a numerical wave tank that can generate the desired wave spectrums. Presently, one of the recent methodologies that have certain intrinsic capabilities for the investigation of free-surface hydrodynamic problems, namely, Smoothed-Particle-Hydrodynamics (SPH) technique, has been utilized for the modelling of a numerical wave tank. The Navier–Stokes and continuity equations are utilized for governing the fluid motion through Weakly Compressible SPH (WCSPH) approach which couples pressure and density by an equation of state. As one of the major numerical treatments, kernel gradient normalization is included into the present SPH method together with the numerical treatments, namely, well-known density smoothing algorithm, hybrid velocity variance-based free surface (VFS), and artificial particle displacement (APD) algorithms. The generation of regular and irregular waves is performed by a moving boundary at the inlet where natural damping is targeted by utilizing a dissipative beach at the end of numerical wave tank. A wide range of test cases in terms of wave-lengths and steepness ratios have been investigated for the regular wave simulations. Although the wave-maker is forced linearly to oscillate sinusoidally at the inlet of the tank, due to the relatively high wave steepness ratios applied, the non-linear character of the free-surface has been clearly observed with the performed Fast Fourier Transform analyses. Wave energy densities of the SPH results have also been compared with the linear theory expectations per unit wave-length. To scrutinize the conditions for the wave-breaking inception, three additional wave steepness values have been simulated at a single wave-length value. As a further examination of the proposed SPH scheme, JONSWAP irregular wave spectrum has been utilized with both flap and piston type moving boundaries. In the light of performed simulations, the proposed SPH numerical scheme can provide robust and consistent results while generating regular and irregular wave systems in deep water conditions. Furthermore, it is observed that it has the capability of capturing the non-linear characteristics of generated waves with high sensitivity, including the wave-breaking phenomenon.