A Coupled Lattice Boltzmann Method and Discrete Element Method for Discrete Particle Simulations of Particulate Flows

Discrete particle simulations are widely used to study large–scale particulate flows in complex geometries where particle–particle and particle–fluid interactions require an adequate representation but the computational cost has to be kept low. In this work, we present a novel coupling approach for such simulations. A lattice Boltzmann formulation of the generalized Navier–Stokes equations is used to describe the fluid motion. This promises efficient simulations suitable for high performance computing and, since volume displacement effects by the solid phase are considered, our approach is also applicable to non–dilute particulate systems. The discrete element method is combined with an explicit evaluation of interparticle lubrication forces to simulate the motion of individual submerged particles. Drag, pressure and added mass forces determine the momentum transfer by fluid–particle interactions. A stable coupling algorithm is presented and discussed in detail. We demonstrate the validity of our approach for dilute as well as dense systems by predicting the settling velocity of spheres over a broad range of solid volume fractions in good agreement with semi–empirical correlations. Additionally, the accuracy of particle–wall interactions in a viscous fluid is thoroughly tested and established. Our approach can thus be readily used for various particulate systems and can be extended straightforward to e.g. non–spherical particles.