为了预报真实液化天然气(LNG)船液舱的共振频率，采用基于直角网格的三维多相流模型，模拟了不同充液水深和激励频率的菱形液舱剧烈晃荡问题．该数值模型采用时间半隐式有限差分法在交错直角网格上求解不可压缩两相流Navier-Stokes(N-S)方程，采用径向基函数虚拟网格法(RBFGCM)处理不规则舱壁结构和，用三维梯度增量水平集(GALS)方法捕捉强非线性自由表面．基于该模型，模拟了横摇激励下的菱形液舱晃荡问题，满意的网格和时间收敛性验证了该方法的高精度和可靠性．而且，不同充液水深下本文冲击压力和波浪爬高结果与实验数据较好地吻合，捕捉到了剧烈的晃荡波浪现象如波浪翻卷．进一步研究了不同水深下舱壁局部位置压力幅值与激励频率之间的关系，确定了菱形液舱共振频率，以期为LNG液舱的结构设计提供理论参考．

To predict the resonance frequency of the real liquefied natural gas (LNG) tank, a Cartesian grid based three-dimensional (3D) multiphase flow model is used to simulate violent sloshing in a prismatic tank at different filling levels and excitation frequencies. In this model, a semi-implicit finite difference method is adopted to solve the incompressible two-phase flow Navier-Stokes (N-S) equations on a staggered Cartesian grid. Besides, a radial basis function ghost cell method (RBFGCM) is used to treat the irregular tank walls and a 3D gradient-augmented level set (GALS) method is used to capture highly nonlinear free surfaces. Based on the present model, the violent sloshing induced by rolling excitations in the 3D prismatic tank is simulated. Satisfactory convergences of grid sizes and time steps demonstrate the high accuracy and reliability of the present method. Moreover, the present results of the impulsive pressure and wave elevation agree well with the experimental data for different filling water depths. In addition, violent sloshing phenomena are captured such as wave rolling. Furthermore, the relationship between the pressure amplitude on the tank wall and the excitation frequency at four filling levels are investigated to identify the resonance frequency of the prismatic tank, to provide theorical guides for structrual design of the tanks.