Numerical simulation of three-dimensional sloshing phenomena using a finite difference method with marker-density scheme

In the present study, three-dimensional sloshing phenomena occurring in liquid cargo tanks are numerically simulated. The Navier-Stokes equations and continuity equation are used for the governing equations, and solved with a finite difference method in a rectangular fixed staggered mesh system. The positions of free surface are defined by the Marker density method satisfying the free-surface boundary conditions, and the flows of the gas and liquid regions are simulated simultaneously. The irregular leg length and star method is employed on the cells near the free surface for the computations of pressure. The computation results are compared with other experimental results to verify the consistency of the present numerical method, and the agreements are reasonably good. Furthermore, the flow characteristics inside a partially filled liquid tank of a real sized ship oscillating regularly and irregularly are computed to verify the possibility of practical application of the present method.