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 about 20 on the particle scale. This direct simulation technique fills a gap between simulations in the viscous regime and high-Reynolds-number modeling. It also combines sufficient computational accuracy with numerical efficiency and allows studies of several thousand, in principle arbitrarily shaped, extended and hydrodynamically interacting particles on regular work stations. We verify the algorithm in two and three dimensions for (i) single falling 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.