Abstract In this paper, a fully Lagrangian formulation for solving rigid–liquid coupling system with free surface is proposed, in which the spatial absolute nodal coordinates and the pressure of liquid are taken as the independent variables, combining the stabilized particle finite element method and multibody algorithms for unified modeling. The virtual contact elements generated in the remeshing process are used to identify the contact nodes on the liquid–solid interface, and the free-slip boundary constraints are imposed by the Lagrange multipliers. For the position deviation of the interface nodes on the concave-curved boundary at a large time step, a position correction strategy is given. In addition, in order to control the numerical dissipation in the simulation, the implicit generalized- α time integration strategy with second-order accuracy is used to solve the differential algebraic equations of the system. Finally, several numerical examples are studied to verify the mass conservation characteristics of the algorithm under coarse mesh and relatively large time steps, and the pressure calculation results are compared with the experimental results reported in the literature, which shows the stability and accuracy of the algorithms proposed.

中文翻译：

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结合多体算法求解自由表面流动问题的绝对节点坐标粒子有限元

摘要 本文提出了以空间绝对节点坐标和液体压力为自变量，结合稳定粒子有限元方法和多体系统求解具有自由表面的刚液耦合系统的全拉格朗日公式。统一建模算法。重新网格划分过程中产生的虚拟接触单元用于识别液固界面上的接触节点，自由滑动边界约束由拉格朗日乘子施加。针对大时间步长下凹曲线边界上界面节点的位置偏差，给出了位置校正策略。此外，为了控制模拟中的数值耗散，采用二阶精度的隐式广义α时间积分策略求解系统的微分代数方程。最后通过几个数值算例验证了算法在粗网格和较大时间步长下的质量守恒特性，并将压力计算结果与文献报道的实验结果进行了对比，表明了算法的稳定性和准确性建议的。