A coupled smoothed finite element method and Lagrangian particle tracking model for three-dimensional dilute particle-laden flows

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 forcedriven 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.