Navier-Stokes simulation with constraint forces: Finite-difference method for particle-laden flows and complex geometries

Building on an idea of Fogelson and Peskin [J. Comput. Phys. 79, 50 (1988)] we describe the implementation and verification of a simulation technique for systems of non-Brownian particles in fluids at Reynolds numbers up to a bout 20 on the particle scale. This direct simulation technique fills a gap between simulations in the viscous regime and high-Reynolds-number modelin g. It also combines sufficient computational accuracy with numerical effici ency and allows studies of several thousand, in principle arbitrarily shape d, extended and hydrodynamically interacting particles on regular work stat ions. We verify the algorithm in two and three dimensions for (i) single fa lling particles and (ii) a fluid flowing through a bed of fixed spheres. In the context of sedimentation we compute the volume fraction dependence of the mean sedimentation velocity. The results are compared with experimental and other numerical results both in the viscous and inertial regime and we find very satisfactory agreement.