000014901 001__ 14901 000014901 005__ 20161115100205.0 000014901 04107 $$aeng 000014901 046__ $$k2016-08-21 000014901 100__ $$aBarker, Thomas 000014901 24500 $$aWell-posed continuum modelling of granular flow 000014901 24630 $$n24.$$p24th International Congress of Theoretical and Applied Mechanics - Book of Papers 000014901 260__ $$bInternational Union of Theoretical and Applied Mechanics, 2016 000014901 506__ $$arestricted 000014901 520__ $$2eng$$aBy 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. 000014901 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb. 000014901 653__ $$a 000014901 7112_ $$a24th International Congress of Theoretical and Applied Mechanics$$cMontreal (CA)$$d2016-08-21 / 2016-08-26$$gICTAM2016 000014901 720__ $$aBarker, Thomas 000014901 8560_ $$ffischerc@itam.cas.cz 000014901 8564_ $$s151565$$uhttps://invenio.itam.cas.cz/record/14901/files/TS.FS08-1.05.pdf$$yOriginal version of the author's contribution as presented on CD, page 3349, code TS.FS08-1.05 . 000014901 962__ $$r13812 000014901 980__ $$aPAPER