A coupled FEM–DEM method for the modeling of fluids laden with particles

This work presents a computational method for the solution of problems involving flowing fluid media laden with solid particles. The idea is based on previous works by the authors on (though then separately considered) fluid–structure interaction and particle dynamics. The fluid problem is treated through an Eulerian finite element approach, with the resulting system of nonlinear equations being iteratively solved by a Newton–Raphson procedure within a Newmark time integration scheme. The particle problem, in turn, is treated through a Lagrangian discrete element approach, wherein both particle-to-particle and particle-to-wall (rigid surfaces) contacts are fully permitted and resolved. The influence of the fluid on the motion of the particles is represented by means of forces and moments, which are computed from solution of the fluid flow around the particles and imposed on the latter in a coupled iterative way. The influence of the particles on the fluid, in turn, is considered by imposing consistent boundary conditions on the fluid at its corresponding interfaces with the particles. This is achieved through an immersed boundaries technique. An implicit, staggered, coupled FEM–DEM scheme is developed within a time-marching solution process. Examples of numerical simulations are provided to illustrate the applicability and potentialities of the proposed method.