Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET

Abstract

Packed bed liquid chromatography is widely applied in academia and industry. Model-based methods are increasingly utilized for process development and optimization, demanding multitudes of complex simulations. We derive spatial arbitrary order discontinuous Galerkin (DG) discretizations for three commonly used chromatography models, including the general rate model (GRM). The methods are integrated in the open source CADET software, making efficient implementations publicly available for the first time. The DG CADET code is validated and benchmarked against the original finite volume CADET code. We observe great performance advantages for DG, depending on the discrete problem size. For a four-component steric mass action GRM, we achieve a speed-up of an order of magnitude for an error range typical for engineering applications. We explore the performance of a collocation Legendre–Gauß–Lobatto (LGL) quadrature DG method in comparison to an exact integration DG method. Our performance benchmarks indicate a slight advantage for collocation DG.