In this paper, the cell-based smoothed finite element method (CS-FEM) empowered by the discrete phase model (DPM) is developed to solve dilute solid particles movements induced by incompressible laminar flow. In the present method, the fluid phase is solved by CS-FEM in the Eulerian framework, while particles are treated as discrete phases traced using Newton's second law in the Lagrangian framework. Meanwhile, the fluidic drag force on particles is considered to realize the one-way coupling of fluid to particles. For the fluid phase, the semi-implicit characteristic-based split (CBS) method is employed to suppress the spatial and pressure oscillations arising from the numerical solution of the Navier-Stokes equations discretized by the CS-FEM. To accurately capture the fluid velocity at an arbitrary particle position inside quadrilateral elements, the mean value coordinates interpolation is introduced. Furthermore, the motion equations for particles are solved by the fourth-order Runge-Kutta method to ensure high accuracy on particle trajectories. Several numerical examples in this paper demonstrate that the proposed method can effectively predict the effect of fluid flow on particle trajectories and position distributions in the analysis of practical and complex flow problems.

在本文中，开发了由离散相模型（DPM）授权的基于单元的平滑有限元方法（CS-FEM），以解决不可压缩层流引起的稀固体颗粒运动。在本方法中，流体相通过欧拉框架中的 CS-FEM 求解，而粒子被视为在拉格朗日框架中使用牛顿第二定律追踪的离散相。同时，考虑流体对粒子的拖曳力，实现流体与粒子的单向耦合。对于流体相，采用半隐式基于特征的分裂（CBS）方法来抑制由CS-FEM离散的Navier-Stokes方程的数值解引起的空间和压力振荡。为了准确捕捉四边形元素内任意粒子位置处的流体速度，引入了平均值坐标插值。此外，粒子的运动方程采用四阶龙格-库塔法求解，以确保粒子轨迹的高精度。本文中的几个数值例子表明，在分析实际和复杂的流动问题时，所提出的方法可以有效地预测流体流动对粒子轨迹和位置分布的影响。