ABSTRACT ABSTRACT: Processes that involve particle-laden fluids are common in geomechanics and especially in the petroleum industry. Understanding the physics of these processes and the ability to predict their behavior requires the development of coupled fluid-flow and particle-motion computational methods. This paper outlines an accurate and robust coupled computational scheme using the lattice-Boltzmann method for fluid flow and the discrete-element method for solid particle motion. Results from several two-dimensional validation simulations are presented. Simulations reported include the sedimentation of an ellipse, a disc and two interacting discs in a closed column of fluid. The recently discovered phenomenon of drafting, kissing, and tumbling is fully reproduced in the two-disc simulation.