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We present a collision model for particle-particle and particle-wallinteractions in interface-resolved simulations of particle-laden flows. Threetypes of inter-particle interactions are taken into account: (1) long- and (2)short-range hydrodynamic interactions, and (3) solid-solid contact. Long-rangeinteractions are incorporated through an efficient and second-order accurateimmersed boundary method (IBM). Short-range interactions are also partlyreproduced by the IBM. However, since the IBM uses a fixed-grid, a lubricationmodel is needed for an inter-particle gap width smaller than the grid spacing.The lubrication model is based on asymptotic expansions of analytical solutionsfor canonical lubrication interactions between spheres in the Stokes regime.Roughness effects are incorporated by making the lubrication correctionindependent of the gap width for gap widths smaller than $\sim 1\%$ of theparticle radius. This correction is applied until the particles reachsolid-solid contact. To model solid-solid contact we use a variant of a linearsoft-sphere collision model capable of stretching the collision time. Thischoice is computationally attractive because it allows to reduce the number oftime steps required for integrating the collision force accurately and isphysically realistic, provided that the prescribed collision time is muchsmaller than the characteristic timescale of particle motion. We verified thenumerical implementation of our collision model and validated it againstseveral benchmark cases for immersed head-on particle-wall andparticle-particle collisions, and oblique particle-wall collisions. The resultsshow good agreement with experimental data.

Collision model for fully-resolved simulations of flows laden with finite-size particles