基于高精度速度势型布西内斯克(Boussinesq)方程对三维液舱内的浅水晃荡现象进行模拟.研究在势流理论框架下进行,总的速度势被分成了两个部分:一部分是在流域内满足拉普拉斯方程且在边界处满足不可穿透条件的特解,而另一部分将由Boussinesq模型求解.数值计算过程中,空间导数离散采用有限差分法,时间步进采用四阶龙格库塔法.首先将三维液舱的长宽比设置为远小于1以模拟二维液舱情况,并与文献的结果对比,验证了数值模型的有效性.三维工况中,各个外部激励频率下,观察到了4种不同的晃荡运动形式,同时在自由面上会观察到相应数量的行进波.此外,讨论了外部激励频率和耦合激励形式对于液舱内晃荡运动形式的影响.

Highly accurate Boussinesq-type equations in terms of velocity potential are used for the simulation of shallow-water sloshing in a three-dimensional tank under the framework of the potential flow theory. The total velocity potential is separated into two parts: one part is a particular solution which satisfies the Laplace equation in the fluid domain and the no-flow condition on the walls while the other part is solved by the Boussinesq-type model. In the process of numerical calculation, the finite difference method is used for spatial derivative discretization and the 4th Runge-kutta method is used for time iteration. To verify the numerical model, the aspect ratio of the tank is set to be much less than 1 for simulation of 2D cases and is compared with the results published. In the 3D cases, four different sloshing motion forms are observed at each external excitation frequency, and a corresponding number of traveling waves are observed on the free surface. Moreover, the effects of external excitation frequency and coupling excitation on the sloshing motion in the tank are discussed.