Implicit-Explicit Methods for the Efficient Simulation of the Settling of Dispersions of Droplets and Colloidal Particles

Abstract

Techniques for the efficient approximate solution of systems of convection-diffusion partial differential equations modelling the sedimentation of droplets of different sizes in a viscous fluid are introduced. These techniques comprise the use of Polynomial Viscosity Matrix (PVM) methods for the convective numerical fluxes and implicit treatment of the nonlinear diffusion terms. Numerical examples based on [A. Abeynaike et al., Chem. Eng. Sci., 79 (2012), pp. 125–137] are presented.