A coupled cell-based smoothed finite element method and discrete phase model for incompressible laminar flow with dilute solid particles

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 semiimplicit 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 fourthorder 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.