A computational approach is presented in this paper for the direct numerical simulation of 3D particulate flows. The given approach is based on the fictitious domain method, whereby the Discrete Element Method (DEM) and the Finite Element Method (FEM) are explicitly coupled for the numerical treatment of particle-fluid interactions. The particle properties are constitutively described by an adhesive viscoelastic model. To compute the hydrodynamic forces, a direct integration method is employed, where the fluid stresses are integrated over the particles’ surfaces. For the purpose of verifying the presented approach, computational results are shown and compared with those of the literature. Finally, the method is applied for the simulation of an agglomeration example.