Front Tracking and Parameter Identification for a Conservation Law with a Space-Dependent Coefficient Modeling Granular Segregation

A well-known experimental setup for the study of segregation by size in a dry granular medium consists of two layers of spheres composed of large and small rigid 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 thereby applies shear to the granular mixture. The spheres will then mix and the large ones rise while the small ones settle in vertical direction. This phenomenon can be modelled by a 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 describes dependence of the shear rate on depth. This model is solved by the hyperfast front tracking method adapted to a conservation law with discontinuous flux. In this way the coefficient can efficiently be identified from experimental observations. Numerical examples are presented.