Efficient lattice Boltzmann simulation of free-surface granular flows with $\mu(I)$-rheology

Abstract

This paper presents a lattice Boltzmann framework for accurate and efficient simulation of free-surface granular flows. The granular assembly is treated as a viscoplastic fluid, whose apparent viscosity varies locally with the shear rate and pressure according to a regularized $\mu(I)$-rheology. A single-phase free-surface model is employed to track the evolution of the particle-air interface. The lattice Boltzmann implementation is first validated by simulating a steady-state granular flow on a rough inclined plane and a good agreement with the analytical solution is achieved. The validated model is then applied to simulate a transient granular column collapse problem. Compared to a companion discrete element simulation, the lattice Boltzmann model with the $\mu(I)$-rheology is able to capture the overall dynamic behaviors of granular column collapse. However, a different behavior is observed when a similar Bingham viscoplastic model with a fixed yield stress is applied, highlighting the pressure dependent nature of granular flows. The proposed lattice Boltzmann formulation is highly efficient compared to the conventional computational fluid dynamics, which has the potential to conduct three-dimensional continuum simulation of large-scale geophysical flows with microscopic granular physics.