Pseudospectral solution of three-dimensional nonlinear sloshing in a shallow water rectangular tank

In this study, a pseudospectral σ-transformation model is developed to simulate fully nonlinear sloshing waves in a three-dimensional shallow water rectangular tank. The σ-transformation maps the physical domain including the water free surface onto a fixed rectangular computational domain. Chebyshev collocation formulae are used to discretize the governing equation and boundary conditions in the computational domain. The numerical model is validated for three well known analytical and numerical sloshing problems. An extensive study is then made of sloshing in a shallow water tank, and the effects of excitation frequency, base aspect ratio, and amplitude of excitation on the wave motions and patterns are considered. Wave regimes and patterns are considerably influenced by the base aspect ratio. In a shallow water tank with a non-square base, different wave regimes are observed during small-amplitude resonant excitation. Also, bores develop during large amplitude resonance excitation. The present study demonstrates that a pseudospectral σ-transformation can accurately model nonlinear sloshing waves in a rectangular tank. Also, results show that contrary to the situation in deeper water tanks, sloshing in shallow water strongly depends on the base aspect ratio.