Three-dimensional simulations of dilute and concentrated suspensions using smoothed particle hydrodynamics

A three-dimensional model for a suspension of rigid spherical particles in a Newtonian fluid is presented. The solvent is modeled with smoothed particle hydrodynamics method, which takes into account exactly the long-range multi-body hydrodynamic interactions between suspended spheres. Short-range lubrication forces which are necessary to simulate concentrated suspensions, are introduced pair-wisely based on the analytical solution of Stokes equations for approaching/departing objects. Given that lubrication is singular at vanishing solid particle separations, an implicit splitting integration scheme is used to obtain accurate results and at the same time to avoid prohibitively small simulation time steps. Hydrodynamic interactions between solid particles, at both long-range and short-range limits, are verified against theory in the case of two approaching spheres in a quiescent medium and under bulk shear flow, where good agreements are obtained. Finally, numerical results for the suspension viscosity of a many-particle system are shown and compared with analytical solutions available in the dilute and semi-dilute case as well as with previous numerical results obtained in the concentrated limit.