Chebyshev super spectral viscosity method for a fluidized bed model

A Chebyshev super spectral viscosity method and operator splitting are used to solve a hyperbolic system of conservation laws with a source term modeling a fluidized bed. The fluidized bed displays a slugging behavior which corresponds to shocks in the solution. A modified Gegenbauer postprocessing procedure is used to obtain a solution which is free of oscillations caused by the Gibbs–Wilbraham phenomenon in the spectral viscosity solution. Conservation is maintained by working with unphysical negative particle concentrations.