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.