Résumé
The objective of this chapter is to describe the interfacing of the Lattice BoltzmannMethod for the simulation of fluids with the Discrete Element Method for the simulation of a collection of rigid particles. For the sake of simplicity, the statistical physics concepts underlying the method are not detailed, and the algorithms are only presented in 2D. The Boltzmann equation is discretized using a standard D2Q9 modelin which the fluid pseudo-particles can move on a lattice with 9 possible directionsof motion. The classical fluid dynamics quantities are defined as sums of local probability densities of finding particles at a specific time and position, and with a given momentum. The Lattice Boltzmann equation is then resolved in two steps. The first step is the so-called Streaming step that consists in computing the advection of the fluid particles. The second step computes the relaxation of the system as a result of possible collisions between fluid particles. Two models are presented for the collision step: the Single Relaxation Time model and the Multiple Relaxation time model.Different boundary conditions are detailed for the implementation of no-slip conditions for the fluid in contact with solid grains or walls (imposed pressure, imposed flow, open boundary conditions and Bounce Back approaches. . . ). Finally, we detail the momentum exchange method for the fluid-grain coupling, and we conclude with examples of simulated systems using this approach.