Front Tracking and Parameter Identification for a Conservation Law with a Space-Dependent Coefficient Modeling Granular Segregation (Advances in Applied Mathematics and Mechanics, 2025)
A well-known experimental setup for the study of segregation by size in adry granular medium consists of two layers of spheres composed of large and smallrigid spheres. These layers are contained within an annular region of concentric cylinders covered above and below by plates. One of the cylinders is rotated and therebyapplies shear to the granular mixture. The spheres will then mix and the large ones risewhile the small ones settle in vertical direction. This phenomenon can be modelled bya conservation law whose flux involves a piecewise constant or smooth coefficient [L.May, M. Shearer, and K. Daniels, J. Nonlin. Sci., 20 (2010), pp. 689–707] that describesdependence of the shear rate on depth. This model is solved by the hyperfast fronttracking method adapted to a conservation law with discontinuous flux. In this waythe coefficient can efficiently be identified from experimental observations. Numericalexamples are presented.