Abstract
Based on the shallow water wave theory, basic equations which describe the nonlinear responses of sloshing are derived, and a numerical method is presented to simulate sloshing phenomena in a rectangular tank which is oscillated horizontally. As the vertical variable isn't contained in the basic equations, the discretization equations are easily obtained. They are the ordinary differential equations of time, which are solved with the Runge-Kutta-Gill Method. The feature in this process is that the dispersion relation included in the basic equations is replaced by that produced by the discretization. In experiments and numerical simulations with small water depths, stable progressive waves are observed, and the surface displacement shows nonlinear responses. Numerical results are in good agreement with experiments, so the applicability of this method is shown.
