DEVELOPMENT OF A NUMERICAL WAVE TANK WITH A CORRECTED SMOOTHED PARTICLE HYDRODYNAMICS SCHEME TO REDUCE NONPHYSICAL ENERGY DISSIPATION

So far, the smoothed particle hydrodynamics (SPH) method has been widely applied in the study of the interactions between water waves and structures. However, nonphysical energy dissipation is a still problem which challenges the simulation of wave-body interactions at large-scale and long duration. For example, in the SPH simulation of wave propagation to a long distance, the wave height could gradually become much smaller than the one generated near the wave maker. To tackle this problem, in this work a kernel correction algorithm is applied to the pressure gradient term in the SPH model, aiming to prevent nonphysical energy dissipation in long time simulations. The kernel correction algorithm is able to ensure the symmetry of the interaction between particle pairs, and therefore, compared with other corrective methods, the present corrected algorithm ensures the conservation of linear momentum and also avoids the complicated treatment at the free surface. Two numerical cases, i.e., the oscillating droplet and wave propagation in a numerical wave tank, are presented to test the accuracy and validity of present corrected SPH algorithm. For the oscillating droplet case, the corrected algorithm is shown to accurately simulate the evolution of the droplet shape, and the kinetic energy is dissipated much slower than traditional SPH models. Through the simulations of regular and irregular wave propagations as well as validations with experimental data, the capability of the corrected SPH algorithm to reduce nonphysical energy attenuation is demonstrated, even for wave propagation at long-term and long-distance conditions. In addition, this algorithm will be shown to be optimal for the SPH simulation at small smooth length, which contributes to save SPH computational cost significantly at three dimensional simulations.