Capturing secondary flows and surface deformation in continuum modeling of dense granular materials using a higher-order rheological model

Capturing secondary flows and surface deformation in dense granular materials, such as those arising from normal stress differences, requires continuum models that extend beyond the first-order scalar μ(I) rheology and include stress terms that are proportional to higher powers of the velocity gradient. In this work, we implement these high-order dense granular rheological models within a scalable, variable-density, two-component continuum incompressible flow solver that supports embedded boundaries to model complex geometries. We apply this framework to simulate dense granular flows in several geometries such as inclined chutes with variable cross sections and converging-diverging nozzles, and systematically examine the influence of high-order rheology on the development of steady state surface curvature and secondary flow patterns. Upon comparison with high-fidelity discrete element method simulations, we find that the higher-order terms are crucial to accurately model surface deformation and secondary vortices, thus demonstrating the accuracy of our rheological models and the continuum numerical method to simulate complex granular flows.