Simulation of water entry into shallow water based on boundary element method

Abstract

The problem of a two-dimensional wedge entering into shallow water is investigated with the boundary element method based on the potential flow theory, and fully nonlinear boundary conditions in time domain are imposed. A stretched coordinate system is used at the initial stage of water entry to avoid the numerical problems originated from extremely small wetted surface. An auxiliary function is used to calculate the pressure on the body surface. The free surface is updated through the fourth order Runge-Kutta scheme. Particularly, a jet cut model is used to avoid the numerical difficulties when the thin and high jet forms. Detailed results through the free surface, pressure distribution and hydrodynamic load at constant speed and prescribed time-varying speed are provided, the comparison with the results from experiments, Wagner theory, semi-analytic method are made and effects of water depth are investigated in detail. It is found that the bottom of the shallow water domain would exert a noticeable effect on the pressure distribution and force of the wedge, especially when the tip of wedge is close to the domain bottom.