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Abstract
In recent years considerable progress has been made in the continuum modelling of granular flows. In particular the μ(I)rheology, which links the local viscosity in a flow to the strainrate and pressure through the nondimensional inertial number I. This formulation greatly benefits from its similarity to the incompressible Navier–Stokes equations as it allows many existing numerical methods to be used. Unfortunately this system of equations is illposed when the inertial number is too high or too low. The consequence of illposedness is that the growth rate of small perturbations tends to infinity in the high wavenumber limit. Due to this, numerical solutions are griddependent and cannot be taken as being physically realistic. In this paper changes to the functional form of the μ(I) curve are considered, in order to maximise the range of wellposed inertial numbers, while preserving the overall structure of the equations. It is found that when the inertial number is low there exist curves for which the equations are guaranteed to be wellposed. However when the inertial number is very large the equations are found to be illposed regardless of the functional dependence of μ on I. A new μ(I) curve, that is
inspired by the analysis of the governing equations and by experimental data, is proposed here. In order to test this regularised rheology, transient granular flows on inclined planes are studied. It is found that simulations of flows, which show signs of illposedness with unregularised models, are numerically stable and match key experimental observations when the regularised model is used. This paper details twodimensional transient computations of decelerating flows, where the inertial number tends to zero, highspeed flows, that have large inertial numbers, and flows which develop into granular rollwaves. This is the first time that granular rollwaves have been simulated in twodimensions, which
represents a major step towards the simulation other complex granular flows.
inspired by the analysis of the governing equations and by experimental data, is proposed here. In order to test this regularised rheology, transient granular flows on inclined planes are studied. It is found that simulations of flows, which show signs of illposedness with unregularised models, are numerically stable and match key experimental observations when the regularised model is used. This paper details twodimensional transient computations of decelerating flows, where the inertial number tends to zero, highspeed flows, that have large inertial numbers, and flows which develop into granular rollwaves. This is the first time that granular rollwaves have been simulated in twodimensions, which
represents a major step towards the simulation other complex granular flows.
Original language  English 

Pages (fromto)  532 
Journal  Journal of Fluid Mechanics 
Volume  828 
Early online date  30 Aug 2017 
DOIs  
Publication status  Published  10 Oct 2017 
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 1 Finished

GLOBAL Manchester Image Reconstruction and ANalysis (MIRAN): Step jumps in imaging by Global Exchange of user pull and method push
Lionheart, W., Cootes, T., Dorn, O., Gray, N., Grieve, B., Haigh, S., Harris, D., Hollis, C., Matthews, J., Mccann, H., Parker, G., Villegas Velasquez, R. & Withers, P.
1/04/12 → 31/03/13
Project: Research