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Frank Platte^{1}, Dmitri Kuzmin^{1}, **Falk Lindner**^{2}, and Stefan Turek^{1}. (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.

References

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Kuzmin, D. and Turek,S., 2004, High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter. J. Comput. Phys, 198, pp 131-158

Kuzmin, D., Möller, M. and Turek, S., 2004, High-resolution FEM-FCT schemes for multidimensional conservation laws. Computer Methods in Applied Mechanics and Engineering, 193, 45-47, 4915-4946

Platte, F., Kuzmin, D., Fredebeul, Chr., Turek, S., 2005, Novel Simulation Approaches for Cyclic Steady-state Fixed-bed Processes Exhibiting Sharp Fronts and Shocks, International Series of Numerical Mathematics, 151, 207-223, Trends and Applications in Constructive Approximation (Eds.) M. G. de Bruin, D. H. Mache & J. Szabados, Birkhäuser Verlag Basel/Switzerland

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