Flows in porous media of fixed arrays of spheres have been studied numerically in the present work. The flow velocity and pressure fields are solved by the lattice Boltzmann method; the no-slip boundary condition at the solid-fluid interface is enforced by the immersed boundary method with the direct forcing scheme. This numerical method, which we call Proteus and initially was developed for simulations of particles in motion, has been extended to study flow over fixed arrays of spheres. The method is validated by comparing the simulated drag coefficient on a single sphere to the one obtained using an empirical drag law. The present method is then applied to obtain the dimensionless drag force on a sphere in both ordered face-centered cubic arrays of spheres and random arrays of spheres. Our results at low solid volume fraction for ordered arrays of spheres show good agreement with the theoretical solution of Hasimoto (1959). A correlation on the drag coefficient at solid fraction ranging from 0 to 0.66 has been derived based on our simulation results. This will help improve the modeling of particulate flows. The case of flow over random arrays of spheres at the solid fraction of 0.345 and flow Reynolds numbers up to 57 has also been studied. Our results agree well with the Ergun’s empirical correlation.

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