Well-posed continuum modelling of granular flow

Abstract eng:
By combining a plastic flow rule with co-linearity of stress and strain-rate, a viscosity is formed that is reflective of dissipation in flowing granular material. Unfortunately, if the ratio of shear and normal stress [1, is taken to be a constant then the equations are always ill-posed [1]. Much experimental evidence is better fit by instead having [1, : MU) [2] where the inertial number I is a non-dimensional grouping of invariant particle and flow properties and is reflective of the deformation time-scales. We present a linear stability analysis of the resultant equations to show that this model is well-posed for intermediate values of I but exhibits unbounded growth of short-wavelength perturbations when flows vary too slowly or too quickly [3]. This makes reliable numerical solution impossible as grid-scale variations will dominate temporal solutions. It is possible to circumvent these issues by considering only steady or shallow flows [4] but additional physical effects should be included to ensure full regularisation.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket