中文摘要：

LBGK结合大涡紊流模型方法应用于粘性流体运动的数值模拟，并在LBGK方法中引入VOF概念，用于跟踪自由表面的运动。利用这种方法计算了贮液容器中粘性流体的自由晃动以及非线性激励下的一阶模态晃动，得到了侧壁上压强分布，并拟合了压力和弯距的估算公式。分析和实践表明，该方法对带自由表面不可压缩流体的数值模拟具有较高的精度。

英文摘要：

The Lattice Bhatnager-Gross-Krook （LBGK） method combined with the large eddy turbulent model is applied to the numerical simulation of the viscous flow, and the Volume of fluid （VOF） concept is introduced into the LBGK method, which is used to simulate the action of the free surface. The free sloshing of the viscous liquid in a tank as well as the first mode sloshing excited by the nonlinear acceleration are simulated. The pressure distribution at the wall of tank is obtained. The e- quations of pressure force and bending moment are fitted. Both the theoretical analysis and the simulation result show that the method in the paper has high precision in the simulation of the incompressible flows with a free surface.