Simulation of non-linear free surface motions in a cylindrical domain using a Chebyshev-Fourier spectral collocation method

When a liquid is perturbed, its free surface may experience highly non-linear motions in response. This paper presents a numerical model of the three-dimensional hydrodynamics of an inviscid liquid with a free surface. The mathematical model is based on potential theory in cylindrical co-ordinates with a rr-transformation applied between the bed and free surface in the vertical direction. Chebyshev spectral elements discretize space in the vertical and radial directions; Fourier spectral elements are used in the angular direction. Higher derivatives are approximated using a collocation (or pseudo-spectral) matrix method. The numerical scheme is validated for non-linear transient sloshing waves in a cylindrical tank containing a circular surface-piercing cylinder at its centre. Excellent agreement is obtained with Ma and Wu's [Second order transient waves around a vertical cylinder in a tank. Journal of Hydrodynamics 1995; Ser, B4: 72-81] second-order potential theory. Further evidence for the capability of the scheme to predict complicated three-dimensional, and highly non-linear, free surface motions is given by the evolution of an impulse wave in a cylindrical tank and in an open domain. Copyright (C) 2001 John Wiley & Sons, Ltd.