Numerical solution of potential flow equations with a predictor-corrector finite difference method

Abstract

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition. A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank. The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function. A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid. The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition. We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion, and the numerical solutions of wave elevation with horizontal excited motion. The beating period and the nonlinear phenomenon are very clear. The numerical solutions agree well with the analytical solutions and previously published results.