Efficient Implicit-Explicit Time Stepping for Accurate and Rapid Simulation of Chromatographic Models

In this paper, we give a summary of recent advances (K. Meyer et al, 2018) on the use of a nodal discontinuous Galerkin finite element (DG-FE) method for spatial discretization of chromatographic models. Explicit Runge-Kutta (ERK) methods are popular for integrating the semi-discrete systems of equations resulting from DG space discretization.

However, ERK methods suffer from stability-based time step restrictions for stiff problems. Therefore, we implement a high order implicit-explicit additive Runge-Kutta (IMEX-ARK) method (Kennedy and Carpenter, 2003, 2007) to overcome system stiffness. The IMEX-RK method advances the non-stiff parts of the model using explicit methods and solve the more expensive stiff parts using an L-stable stiffly-accurate explicit, singly diagonally implicit Runge-Kutta method (ESDIRK).

We show that for a multicomponent nonlinear chromatographic system, the IMEX-ARK scheme becomes more efficient than explicit methods for increasingly stiff systems. We recommend integrating the convective term using explicit methods and to integrate both the diffusive and reactive terms using implicit methods.