Finite element simulation of three-dimensional particulate flows using mixture models

In this paper, we discuss the numerical treatment of three-dimensional mixture models for (semi-)dilute and concentrated suspensions of particles in incompressible fluids. The generalized Navier-Stokes system and the continuity equation for the volume fraction of the disperse phase are discretized using an implicit high-resolution finite element scheme, and maximum principles are enforced using algebraic flux correction. To prevent the volume fractions from exceeding the maximum packing limit, a conservative overshoot limiter is applied to the converged convective fluxes at the end of each time step. A numerical study of the proposed approach is performed for 3D particulate flows over a backward-facing step and in a lid-driven cavity.