Efficient lattice Boltzmann simulation of free-surface granular flows with μ(I)-rheology

Abstract

<p>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 u(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 u(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 <a href="https://www.sciencedirect.com/topics/physics-and-astronomy/computational-fluid-dynamics" title="Learn more about computational fluid dynamics from ScienceDirect's AI-generated Topic Pages">computational fluid dynamics</a>, and has the potential to conduct three-dimensional continuum simulation of large-scale geophysical flows with microscopic granular <a href="https://www.sciencedirect.com/topics/physics-and-astronomy/physics" title="Learn more about physics from ScienceDirect's AI-generated Topic Pages">physics</a>.<br></p>