High-order approximation of chromatographic models using a nodal discontinuous Galerkin approach

Abstract

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Numerical approximations of chromatographic models

“…Example 4.3. In this example, we compare our simulation with the test given in [14], section 4.22. The parameters are chosen from Table 5 with N t = 5000.…”

“…The authors validate their scheme against other flux-limiting schemes available in the literature. To see about discontinuous Galerkin approximation for system (2.1) we refer to [11,14,15]. Recently in [19] a transport model is used to describe gradient elution in liquid chromatography.…”

“…Figure 1 shows both analytical solution and approximated solution with the numbers of spatial steps n x = 100 and of temporal steps n t = 400. Table 2 gives a comparison of L 1 -error and CPU time of our method with discontinuous Galerkin finite element method (DG-FE) with linear basis functions in [10,11] and with high order basis function of order 8 from [14].…”

A stabilized nodal spectral solver for liquid chromatography models

“…Then, the Gibbs phenomenon is of less concern and arbitrary high-order methods can be used for cost-efficient simulations. Therefore, we (Meyer et al (2018)) suggested to use a hp-type DG method, proposed by Warburton (2002, 2008), to cost-efficiently predict realistic chromatographic systems. In short, the computational domain is partitioned into non-overlapping elements while the solution within an element is approximated by an pth order polynomial.…”

ChromaTech: A discontinuous Galerkin spectral element simulator for preparative liquid chromatography

“…ChromaTech is based on a discontinuous Galerkin spectral element method in nodal form (Hesthaven andWarburton, 2002, 2008), that allows arbitrary high-order (spectral) convergence within elements while retaining stability of the method (Meyer et al, 2018b(Meyer et al, , 2019. Moreover, the method is massconservative and can be naturally extended to support mesh refinement with adaptive element sizes and polynomial orders (hp-adaptivity), see e.g.…”