Numerical simulation of 2D sloshing waves using SPH with diffusive terms

A numerical model based on the Smoothed Particle Hydrodynamics (SPH) method is developed which can appropriately simulate two-dimensional (2D) sloshing waves starting from smooth harmonic to violent breaking waves in a partially filled rectangular water container. This is achieved by employing a single set of numerical tools for solving the fluid flow problem under given boundary conditions. Recently, δ-SPH model has been proven to be superior to standard SPH for solving fluid flow problems covering a broad range of Reynolds (Re) numbers including violent fluid motion involving free surface fragmentation. Present work extends this further by applying δ-SPH to non-violent sloshing waves with specific focus in capturing higher order harmonics as generally predicted by an analytical or potential flow based model. An in depth analysis has been carried out to identify major factors affecting the present δ-SPH model from predicting higher order harmonics. The role of XSPH factor as used in SPH in smoothening of velocity has further been revisited to investigate its' effect on pressure, particularly in violent sloshing flows. Inter-comparison has been performed with few other SPH versions (namely, fully incompressible SPH (ISPH) and f-SPH, apart from standard weakly compressible SPH (WCSPH)) for selected cases. The model prediction for different physical quantities of sloshing has been found to be in good agreement with results from other experimental, numerical and analytical based studies. Based on the present study, suitable scales for the tuning factors have been proposed for the development of robust SPH models which is expected to simulate sloshing waves defined by relatively broader d/L (ratio of initial water depth to tank length) ranges.