Linearly implicit-explicit schemes for the equilibrium dispersive model of chromatography

Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of different solute components. This property calls for numerical methods with shock capturing capabilities. Based on results by Donat, Guerrero and Mulet (Appl. Numer. Math. 123 (2018) 22-42), conservative shock capturing numerical schemes can be designed for this chromatography model. Since explicit schemes for diffusion problems can pose severe stability restrictions on the time step, the novel schemes treat diffusion implicitly and convection explicitly. To avoid the need to solve the nonlinear systems appearing in the implicit treatment of the nonlinear diffusion, second-order linearly implicit-explicit Runge-Kutta schemes (LIMEX-RK schemes) are employed. Numerical experiments demonstrate that the schemes produce accurate numerical solutions with the same stability restrictions as in the purely hyperbolic case.