Abstract The Boussinesq-type equations in terms of velocity potential are adopted for the solutions of three-dimensional nonlinear sloshing motions in a shallow-water rectangular tank. The total velocity potential is divided into two parts: a particular solution and the rest which is calculated by the Boussinesq-type equations. Particular solutions of six degrees of freedom motions are constructed. The fully nonlinear free surface boundary conditions are satisfied and finite difference scheme is adopted for the spatial derivatives. The free surface profiles in tank with external excitation frequencies close to the first natural frequency are presented. Numerical results demonstrate that the Boussinesq-type equations with particular solutions can accurately model nonlinear sloshing waves in shallow-water rectangular tank.

中文翻译：

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浅水矩形水槽三维非线性晃荡数值研究

摘要 采用Boussinesq型速度势方程求解浅水矩形水箱三维非线性晃荡运动。总速度势分为两部分：一个特解，其余部分由 Boussinesq 型方程计算。构造了六个自由度运动的特定解。满足完全非线性自由表面边界条件，空间导数采用有限差分格式。给出了外部激励频率接近第一固有频率的水箱中的自由表面轮廓。数值结果表明，具有特解的Boussinesq型方程可以准确地模拟浅水矩形水槽中的非线性晃荡波。