Continuum simulation of the discharge of the granular silo: a validation test for the mu(I)-visco-plastic flow law

TL;DR

This study validates a continuum mu(I)-visco-plastic flow law for granular silo discharge by comparing it with discrete Contact Dynamics simulations, showing good qualitative agreement especially in rapid flow regions.

Contribution

It demonstrates the effectiveness of the mu(I)-flow-law in continuum models to qualitatively replicate granular silo discharge behavior, highlighting the importance of inertial number dependence.

Findings

Good agreement in rapid flow regions for velocity and pressure.

Discrepancies in slow creep regions, but bulk deformation matches.

Parameter dependence of mu(I)-flow-law is crucial for quantitative accuracy.

Abstract

Using both a continuum Navier-Stokes solver, with the mu(I)-flow-law implemented to model the viscous behavior, and the discrete Contact Dynamics algorithm, the discharge of granular silos is simulated in two dimensions from the early stages of the discharge until complete release of the material. In both cases, the Beverloo scaling is recovered. We first do not attempt quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement is obtained in the regions of rapid flows, while areas of slow creep are not entirely captured by the continuum model. The pressure field shows a general good agreement. The evolution of the free surface implies differences, however, the bulk deformation is essentially identical in both approaches. The influence of the parameters of the mu(I)-flow-law is systematically investigated, showing the importance of the dependence on the inertial number I to achieve quantitative agreement between continuum and discrete discharge. The general ability of the continuum model to reproduce qualitatively the granular behavior is found to be very encouraging.