Liquid-solid two-phase flow with free surface is a significant issue in nature and engineering fields. In present study, an in-house solver MPSDEM-SJTU based on a fully Lagrangian coupled method is developed to solve the problems of liquid-solid two-phase flows. The improved moving particle semi-implicit (IMPS) method is applied for the simulation of incompressible viscous liquid flows while the discrete element method (DEM) is used to model the interaction among the solid particles. The coupling strategy is based on the local averaging technique. Multiple time-step algorithm is adopted for those two methods to balance the stability and the efficiency. The free surface detection and the solid-fluid neighbor search are modified. A simulation of multi-balls collapse is conducted to verify the DEM program of the present solver. The distributions of solid balls at different instants are in good agreement with the experimental results. Then, this solver is applied for two typical problems of two-phase flows, including the two-phase dam-break and the liquid-solid flows in a rotating cylindrical tank. The flow front, flow patterns and the shape of solid beds all agree well with experimental observations.

具有自由表面的液固两相流动是自然界和工程领域的一个重要问题。在目前的研究中，开发了一种基于完全拉格朗日耦合方法的内部求解器 MPSDEM-SJTU 来解决液固两相流问题。改进的移动粒子半隐式（IMPS）方法用于不可压缩粘性液体流动的模拟，而离散元方法（DEM）用于模拟固体粒子之间的相互作用。耦合策略基于局部平均技术。这两种方法采用多时间步长算法来平衡稳定性和效率。修改了自由表面检测和固液邻域搜索。进行多球坍塌的模拟以验证本求解器的 DEM 程序。实心球在不同时刻的分布与实验结果吻合较好。然后，将该求解器应用于两相流的两个典型问题，包括两相溃坝和旋转圆柱罐中的液固流。流动前沿、流动模式和固体床的形状都与实验观察一致。