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We consider a stationary problem for the Navier-Stokes equations in a domain Ω ⊂ R 2 with a finite number of "outlets" to infinity in the form of infinite sectors. In addition to the standard adherence boundary conditions, we prescribe total fluxes of velocity vector field in each "outlet", subject to the necessary condition that the sum of all fluxes equals zero. Under certain restrictions on the aperture angles of the "outlets", which seem close to being necessary, we prove that for small fluxes this problem has a solution which behaves at infinity like the Jeffery-Hamel flow with the same flux, and we prove that this solution is unique in the class of solutions satisfying the energy inequality (4.4). We also study the problem with another type of additional condition at infinity, that which involves limiting values of the pressure at infinity in the outlets. Finally, we present a simplified construction of a small Jeffery-Hamel solution with a given flux based on the contraction mapping principle.

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.