An adaptive refinement neural particle method for granular flows

Granular flows are challenging for numerical simulations due to their complex dynamics and potential numerical stability issues. The μ(I)-rheology is a popular continuum mechanics-based model for describing the granular behavior in the dense regime. In this study, we propose an adaptive refinement neural particle method (arNPM), which consists of novel Lagrangian physics-informed neural networks (PINNs) that incorporate the μ(I)-rheology for modeling granular flows. There are two key features of the proposed arNPM approach. First, the high-order derivatives inherent in the μ(I)-rheology are solved straightforwardly by automatic differentiation (AD), which is a peculiar advantage of PINNs. Second, this approach, equipped with an adaptive refinement feature, allows for the visualization of realistic particle flow patterns and well captures evolving free surfaces. The dependability of the method is tested against transient surface flow simulations in wide and narrow channel geometries. Thereafter, it is applied to granular column collapses with varying aspect ratios, where results show excellent agreement with experiments for both surface evolution and wavefront propagation. Comparisons between the frictional and frictionless sidewalls clearly show the importance of considering the sidewall resistances, especially for the cases with high initial aspect ratios. Moreover, inference particle visualization allows a realistic description of the particle trajectories and different granular flow behaviors, including solid-like cores and fluid-like spreading. These results enable a deeper understanding of the sidewall effects for dam-break type simulations and highlight the capabilities of the proposed arNPM to capture the complex granular flow dynamics, which are often difficult to extract from conventional numerical results.