Regular Article: Direct Simulations of 2D Fluid-Particle Flows in Biperiodic Domains

We propose a method to simulate the motion of 2D rigid particles in a viscous, incompressible fluid. Within the arbitrary Lagrangian Eulerian framework, momentum equations for both the fluid and the particles are discretized, and a coupled variational formulation is established. By introducing an appropriate finite element approximation, a symmetric linear system is obtained. This system is solved by an inexact Uzawa algorithm. The main interest of such simulations lies in the average behaviour of a high number of particles. We therefore introduced a biperiodic formulation of the problem, which makes it possible to represent many-body mixtures at a reasonable computational cost. In order to model realistic situations, an extra term must be added to the pressure. This extra term is shown to be the lagrange multiplier associated with the vertical volume conservation constraint. We developed an appropriate unstructured mesh generator, so that the biperiodicity of the fields can be treated in a strong sense. The question of particle contact is addressed, and a simple technique to overcome numerical problems is proposed. The influence of periodic lengths is investigated through different simulations. The same case is simulated for different sizes of the window, and the behaviour of some space-averaged quantities is studied.