Abstract: A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equations with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equations of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

Key words: viscous drop, axisymmetric Stokes flow, rigid wall, motion and deformation, stress, boundary integral method, three-dimensional (3D) nonlinear potential flow equation, predictorcorrector finite difference method, staggered grid, nested iterative method, 3D sloshing