Mater.Phys.Mech.(MPM)
No 1, Vol. 35, 2018, pages 21-27

ON THE NUMERICAL SOLUTION OF A VARIABLE-COEFFICIENT BURGERS
EQUATION ARISING IN GRANULAR SEGREGATION

I.C. Christov

Abstract

We study a variable-coefficient Burgers equation arising in the modelling of segregation of dry bidisperse granular mixtures. The equation is subject to nonlinear boundary conditions for the particle flux. We construct a strongly implicit Crank.Nicolson type of numerical scheme for the latter equation. The scheme is benchmarked against a standard exact solution of kink type, showing second-order of accuracy and good discrete conservation properties. Two segregation problems considered in the literature are then solved and discussed. The first is the case of a linear kinetic stress profile, which renders the governing equation of constant-coefficient type, while the second is the case of a variable kinetic stress profile based on an expression fit to particle dynamics simulation data.

Keywords: Burgers equation; implicit finite-difference scheme; granular segregation.

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