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This paper presents a numerical study on suspensions of monodisperse non-Brownian grains in a Couette flow. The fully resolved coupled smoothed particle hydrodynamics and discrete element method is employed to model the motion of arbitrarily shaped grains in a viscous fluid. The numerical method is benchmarked against its capability in accurately handling grain–fluid hydrodynamics and inter-grain collisions. It is then used to simulate suspension flows of varying particle Reynolds and Bagnold numbers subjected to different shear rates, solid concentrations, and solid-to-fluid density ratios. A special focus is placed on the effect of grain shape with different aspect ratios and convexities on the flow behavior. Both the inertia and the grain shape are found to affect the grain–fluid and inter-grain interactions and uniquely contribute to the overall shear stress and the rheology of the suspension. The local profiles of solid concentration suggest the presence of grain layering near the boundary walls, which becomes more pronounced with higher solid concentration and inertia, and increased non-circularity in grain shape. A further examination of the pair distribution function and average particle rotation reveals a strong correlation between suspension viscosity and grain microstructure and kinematics. [ABSTRACT FROM AUTHOR]