|
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. |
full paper (pdf, 1456 Kb)