On linearly implicit IMEX Runge-Kutta methods for degenerate convection-diffusion problems modeling polydisperse sedimentation

Abstract

Implicit-explicit (IMEX) Runge-Kutta (RK) methods are suitable for the solution of nonlinear, possibly strongly degenerate, convection-diffusion problems, since the stability restrictions, coming from the explicitly treated convective part, are much less severe than those that would be deduced from an explicit treatment of the diffusive term. A particularly efficient variant of these schemes, so-called linearly implicit IMEX-RK schemes, arise from discretizing the diffusion terms in a way that more carefully distinguishes between stiff and nonstiff dependence, such that in each time step only a linear system needs to be solved. These schemes provide an efficient tool for the numerical exploration of sediment formation and composition under a strongly degenerate polydisperse sedimentation model.