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Stabilisation of Convection Dominated Problems for the Direct Calculation of Cyclic Steady States of Chemical Processes

Frank Platte1, Dmitri Kuzmin1, Falk Lindner2, and Stefan Turek1. (1) Institute of Applied Mathematics, University of Dortmund, Vogelpothsweg 87, Dortmund, 44227, Germany, (2) Bio- and Chemical Engineerung, University of Dortmund, Emil-Figge-Str 66, Dortmund, 44227, Germany

The field of chemical engineering has received an increasing interest in unsteady-state processes. Some of them exhibit instationary behaviour especially when based on periodically operated conditions. Typical candidates among these are the reverse-flow-reactor, the chromatographic reactor and the adsorptive reactor. Since the underlying regeneration strategy is nearly always based on cycles -- e.g. a reaction cycle is followed by a regeneration cycle and so on -- the overall temporal behaviour of such processes eventually develop into cyclic steady states (after a transient phase). Experiments reveal a slow transient behaviour into the cyclic steady-state. This can also be observed in simulations based on conventional numerical treatment such as the method of lines. In addition to this problem many instationary processes exhibit sharp fronts or even shocks which require stabilisation of the convective terms. In this work we present a method of combining the idea of global discretisation with modern stabilisation techniques of types FEM-FCT and FEM-TVD in order to obtain an efficient, well approximating and robust tool for the general simulation of instaionary and in particular cyclic-steady-state processes.


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