An optimization-based discrete element model for dry granular flows: Application to granular collapse on erodible beds

Numerical simulations of granular dam break: Comparison between discrete element, Navier-Stokes, and thin-layer models

“…The best-fit interparticle friction coefficient is µ p = 0.9. Note that this value is relatively large compared to the friction coefficient µ p = 0.3, calibrated by comparing 3D simulations and experiments [52], and which is in the range of friction coefficients measured for a perfect glass/glass contact µ p = 0.4 [70], and that measured with MD µ p = 0.16 [71]. In COCD, this difference in calibrated friction coefficients arises when comparing mass profiles in 2D and 3D simulations.…”

“…Numerous numerical methods have been proposed for CD models [24,26,52,[63][64][65][66][67][68]. Classically, one shall specify the normal and tangential contact laws, which must be verified for every contact and time step (Fig.…”

“…In this paper, to compute the approximated solution of the motion equation including the contact laws ( 1) and ( 2), we use the numerical method called Convex Optimization Contact Dynamics (COCD), described in [52]. In this particular approach, the numerical scheme is a natural discretization of Newton's second law and the non-overlapping constraint (1) is convexified.…”

“…More precisely, the macroscopic static friction coefficient µ s = tan(θ m ) -where θ m is the static friction angle, i.e., the angle that the granular mass forms at rest -can be interpreted as the combination of the inter-particle friction coefficient µ p and the geometric trapping (dilatancy effect) µ g [69]. The coefficient µ g is linked to the grains' shapes, masses, or inertia, while µ p is a given parameter of the model, and used in the classical Coulomb's law of friction at any grain/grain or grain/wall contact [52].…”

“…We then compare our 2D simulations, keeping, when possible, as a common reference the experiments (performed under 3D experimental conditions) of Farin et al (2014) [17]. We investigate the discrepancies between discrete, Navier-Stokes and thin-layer models, with three numerical codes: the discrete model Convex Optimization Contact Dynamics (COCD) [52], the Navier-Stokes model Basilisk [53], and the thin-layer model SHALTOP [20,[54][55][56][57]. In order to allow for a more straightforward interpretation, we consider the simple case of a 2D granular dam break, reproducing the 3D experiments of [17] for three slope angles θ = 0 • , 10 • and 16 • .…”