We developed a model for inexpensive Direct Numerical Simulations of particle-laden flow by fully resolving the hydrodynamics at all times except when the gap between colliding particles becomes comparable to the grid step. The resolved hydrodynamics were obtained with a previously developed pressure boundary integral method for direct fluid-particle simulations on Cartesian grids. The unresolved part of the lubrication pressure/shear force in the subgrid gap was predicted using theoretical Stokes flow models. Singular lubrication forces were avoided by postulating that contact begins when the gap distance between the particles becomes equal to the size of micro-asperities. The mechanical contact between particles is dynamically resolved and particle interactions are both inelastic and frictional. The proposed numerical model was validated through resolution tests and comparison with experimental data for immersed binary collisions. Published by Elsevier Ltd.