We present a particle-resolved simulation method for analyzing the rheology of suspensions consisting of noncolloidal, monodisperse, spherical particles dispersed in an incompressible Newtonian fluid. The method employs the lattice Boltzmann method for fluid flow and the discrete element method for particle dynamics, coupled through the improved smoothed profile approach. Lees–Edwards (LE) boundary conditions are implemented to enable efficient simulations of suspensions under shear flow. Verification tests confirm the correct implementations of the LE boundary conditions and the method for evaluating the apparent viscosity of suspensions. Applications to suspension shear flows over a wide range of particle volume fractions and interparticle friction coefficients show good agreement with previous experimental and numerical results, and capture the transition in the dominant mechanisms controlling suspension viscosity with increasing particle volume fraction, from the suspending fluid viscosity, to fluid–particle hydrodynamic interactions, and finally to particle–particle direct contacts. These results demonstrate that the proposed method provides an efficient, robust, and accurate tool for numerical investigations of suspension rheology.

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• Fluid-particle interactions
• Complex fluids
• Suspensions
• Lattice-Boltzmann methods