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We study a variable-coefficient Burgers equation arising in the modelling ofsegregation of dry bidisperse granular mixtures. The equation is subject tononlinear boundary conditions for the particle flux. We construct a stronglyimplicit Crank--Nicolson type of numerical scheme for the latter equation. Thescheme is benchmarked against a standard exact solution of kink type, showingsecond-order of accuracy and good discrete conservation properties. Twosegregation problems considered in the literature are then solved anddiscussed. The first is the case of a linear kinetic stress profile, whichrenders the governing equation of constant-coefficient type, while the secondis the case of a variable kinetic stress profile based on an expression fit toparticle dynamics simulation data.

On the numerical solution of a variable-coefficient Burgers equation arising in granular segregation