In this study, a coupled solution algorithm for three-dimensional dilute particle-laden flows is proposed by integrating the Lagrangian particle tracking model into the smoothed finite element method (S-FEM). Initially, an unstructured mesh fluid solver with multi-type elements is developed using the cell-based S-FEM (CS-FEM) in the Eulerian framework. Subsequently, a fluid force-driven strategy is employed to trace the particle trajectories based on the Lagrangian approach. Moreover, a one-way coupling strategy is designed to perform the solution of the particle-fluid system. To ensure accurate computation of fluid information at the particle positions, we introduce the spherical mean value interpolation algorithm that is compatible with polyhedral elements, enabling uniform interpolation across different types of elements. The correctness of both the Eulerian and Lagrangian solvers is validated independently using benchmarks. Numerical results, validated by references and the finite volume method (FVM) software Fluent, demonstrate the effective prediction of particle trajectories and distributions by the proposed algorithm. Overall, this algorithm expands the application of CS-FEM to multiphase flows and exhibits its capability to handle practical particle-laden flow problems.

中文翻译：

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三维稀颗粒负载流的耦合平滑有限元法和拉格朗日颗粒跟踪模型

在本研究中，通过将拉格朗日粒子跟踪模型集成到平滑有限元法（S-FEM）中，提出了三维稀颗粒负载流的耦合求解算法。最初，使用欧拉框架中基于单元的 S-FEM (CS-FEM) 开发了具有多类型元素的非结构化网格流体求解器。随后，采用流体力驱动策略基于拉格朗日方法追踪粒子轨迹。此外，设计了一种单向耦合策略来执行颗粒-流体系统的求解。为了保证粒子位置处流体信息的精确计算，我们引入了与多面体单元兼容的球均值插值算法，能够在不同类型的单元之间进行统一插值。欧拉和拉格朗日求解器的正确性均使用基准进行独立验证。数值结果经参考文献和有限体积法（FVM）软件 Fluent 验证，证明了所提出的算法对粒子轨迹和分布的有效预测。总体而言，该算法扩展了 CS-FEM 在多相流中的应用，并展示了其处理实际含颗粒流问题的能力。