Sloshing simulation of standing wave with time-independent finite difference method for Euler equations

The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional (2D) tank are studied. The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid. A time-independent finite difference method, which is developed by Bangfuh Chen, is used to solve the Euler equations for incompressible and inviscid fluids. The numerical results agree well with the analytic solutions and previously published results. The sloshing profiles of surge and heave motion with initial standing waves are presented. The results show very clear nonlinear and beating phenomena.