Regularising granular flow rheology

Tom Barker (The University of Manchester)

ATB Frank Adams 1,

In recent years considerable progress has been made in the continuum modelling of granular flow. In particular the now ubiquitous μ(I)-rheology (Jop, Forterre & Pouliquen, 2005) which benefits from a strong resemblance to the incompressible Navier–Stokes equations albeit with a pressure and strain-rate dependant viscosity. Unfortunately this system of equations is ill-posed (Barker, Schaeffer, Bohorquez & Gray, 2015) when the inertial number I is too high or too low. These limits correspond to fast and slow deformations respectively and so this issue precludes the simulation of flows involving such dynamics. It is therefore vital to discuss the potential approaches for regularising the equations and explore the possibility of maintaining the currently implemented numerical methods for the full range of inertial numbers. 

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