A Continuum Framework for Modeling Frictional-Collisional Interactions in Bed-Load Transport: Insights from Discrete Element Simulations

We have investigated the modeling of collisional bed-load transport with a focus on continuum approaches for granular flow. A frictional-collisional framework, combining the Coulomb model and the kinetic theory of granular flows, is proposed to address the limitations of classical kinetic theory, which fails to accurately reproduce results from coupled fluid–discrete simulations. These discrepancies are attributed to assumptions of negligible interparticle friction and the absence of a saltation model in continuum formulations. 

To guide model development, the fluctuating energy balance obtained from discrete simulations is systematically compared with kinetic theory predictions. The analysis reveals that interparticle friction significantly affects the radial distribution function and increases energy dissipation, aligning with previous findings. Additionally, a saltation regime is identified, causing deviations from the viscosity and pseudo-thermal diffusivity laws of kinetic theory in dilute regimes. 

Building on these insights, the two-fluid model is modified to incorporate interparticle friction and coupled with a saltation model. The results demonstrate that for inelastic, frictional particles, interparticle friction primarily governs energy dissipation, and the macroscopic granular flow behavior is independent of microscopic particle properties. The enhanced model successfully reproduces the 𝜇(𝐼) rheology in the dense regime of granular flow. Experimental validation confirms significant improvements in predicting granular flow behavior, highlighting the model’s effectiveness in capturing key physical processes.