In this paper, a new Lagrangian differencing dynamics (LDD) method is presented for the simulation of granular flows. LDD is a truly meshless method, which employs second-order consistent spatial operators derived from the Taylor expansion and point renormalization. A decoupled pressure-velocity formulation is employed to derive the pressure Poisson equation, which ensures smooth pressure results in time. Granular media are modeled as viscoplastic materials with the Drucker-Prager yield surface. The velocity equation is formulated and solved in an implicit form, in order to handle large viscosities from the constitutive model. Furthermore, a position-based dynamics technique is used to maintain uniform distribution of the Lagrangian points. The presented LDD method for granular flows is validated by simulating two numerical examples. The results are compared with experimental and numerical data from the literature.

在本文中，提出了一种新的拉格朗日差分动力学（LDD）方法来模拟颗粒流。LDD 是一种真正的无网格方法，它采用从泰勒展开和点重整化导出的二阶一致空间算子。解耦压力-速度公式用于推导压力泊松方程，确保及时获得平滑的压力结果。颗粒介质被建模为具有 Drucker-Prager 屈服面的粘塑性材料。速度方程以隐式形式进行公式化和求解，以便处理来自本构模型的大粘度。此外，基于位置的动力学技术用于保持拉格朗日点的均匀分布。通过模拟两个数值例子验证了所提出的用于颗粒流的 LDD 方法。