Dense particle-laden flows play an important role in many environmental processes, including the shaping of rivers and the formation of landslides. Despite decades of study, researchers have not been able to accurately predict the onset of erosion and the amount of sediment transported by flows, due in part to the difficulty in measuring dense particle-laden flows. Highly-resolved numerical simulations, on the other hand, allow us to study the physics of particle-fluid and particle-particle interactions in much more detail.

We develop a code to accurately simulate dense, polydisperse, particle-laden flows as well as methods by which to analyze them. The code solves the Navier-Stokes equations for the fluid phase and resolves the flow around each individual particle using an immersed boundary method. We also develop a collision model to accurately resolve particle-particle interactions within the fluid. We then perform simulations of a pressure-driven flow over a bed of spherical particles that agree with experimental results for particle velocities and flow rates. Using a control volume momentum balance, we analyze fluid and particle stresses within the simulations, which reveal the mechanisms by which the particle bed expands and contracts during changes in flow rates. These same stresses also allow us to measure the rheology of the particle-laden flows, where we find some agreement with existing constitutive models but also reveal the need to develop these models further.