In this paper, a multiphase moving particle semi-implicit (MPS) method is developed by introduction of various multiphase models into the original MPS method for single-phase flows, and is then applied to the numerical simulations of two-layer-liquid and three-layer-liquid sloshing in a 2-D rectangular tank under different external excitations. To validate the accuracy of the present multiphase MPS method, the qualitative and quantitative results, including wave profiles, interface elevations and impact pressures, are compared with experimental data and other numerical results, which show a good agreement. In particular, the evolutions of free surface and phase interfaces are compared and an obvious discrepancy is found, indicating that the phase interfaces may suffer from complex deformations while the free surface keeps relatively quiet. Moreover, the different modes of phase interface are observed under different excitation frequencies. Then, the violent sloshing of a three-layer-liquid system is simulated and the phenomenon of internal wave breaking is well captured, which mainly benefitted from the Lagrangian basis of MPS method and its advantage in multiphase flows with complex interfaces. Finally, the three-layer-liquid sloshing with a vertical baffle are simulated to investigate the suppressing effect of baffle on multi-layer-liquid sloshing.

在本文中，通过将各种多相模型引入到单相流的原始 MPS 方法中，开发了一种多相运动粒子半隐式 (MPS) 方法，然后将其应用于两层液体和三层流体的数值模拟。不同外部激励下二维矩形罐中的层液晃动。为了验证当前多相 MPS 方法的准确性，将定性和定量结果，包括波浪剖面、界面高程和冲击压力，与实验数据和其他数值结果进行了比较，显示出良好的一致性。特别是，比较了自由表面和相界面的演变，发现了明显的差异，表明相界面可能遭受复杂的变形，而自由表面保持相对安静。此外，在不同的激励频率下观察到不同的相位界面模式。然后，模拟了三层液体系统的剧烈晃动，很好地捕捉了内波破碎现象，这主要得益于MPS方法的拉格朗日基础及其在复杂界面多相流中的优势。最后，模拟了带有垂直挡板的三层液体晃动，研究了挡板对多层液体晃动的抑制作用。这主要得益于 MPS 方法的拉格朗日基及其在具有复杂界面的多相流中的优势。最后，模拟了带有垂直挡板的三层液体晃动，研究了挡板对多层液体晃动的抑制作用。这主要得益于 MPS 方法的拉格朗日基及其在具有复杂界面的多相流中的优势。最后，模拟了带有垂直挡板的三层液体晃动，研究了挡板对多层液体晃动的抑制作用。