Finite element simulation of complex dense granular flows using a well-posed regularization of the μ(I)-rheology

Abstract

Dense granular flows play an important role in industry and nature. Numerical simulation is a helpful tool to understand their behavior. The high particle concentration in a particle-laden flow leads to non-Newtonian fluid properties. The μ(I)-rheology is a constitutive model to describe a complex, unconventional viscoplastic, shear-thinning flow behavior that agrees well with experiments of dense granular flow. This constitutive model is based on the Coulomb [1] friction and assumes that the pressure is proportional to the tangential stress and related to it by a friction parameter. The friction parameter depends on a dimensionless inertial number I which describes the macroscopic and microscopic timescales of the particle rearrangement. Barker et al. [2] showed that the constitutive equations of the μ(I)-rheology are ill-posed for low and high inertial number regimes. This often results in instabilities, oscillations and high sensitivity of the solution to input parameters. We apply a partial regularization proposed by Barker and Gray [3] for a finite element simulation of a 2D and 3D column collapse with the intention to get stable results and show the disadvantageous outcome of ill-posed constitutive equations. Here, we use a Navier-Stokes solver and the volume-of-fluid method to describe the interface between a dense granular column and a light surrounding fluid. The implementation is done in libMesh using the residual-based variational multiscale method. The objective of this study is to analyze the effects of the partial regularization on the computational simulation of a column collapse using the finite element method. We observe that the viscosity field using the partially well-posed regularized formulation of the μ(I)-rheology by Barker and Gray [3] has a smoother distribution and no spurious oscillations or shear bands, even in simulations with high density and viscosity contrasts.