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By H. G. Othmer (auth.), Professor Dr. Klaus H. Ebert, Professor Dr. Peter Deuflhard, Professor Dr. Willi Jäger (eds.)

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Additional resources for Modelling of Chemical Reaction Systems: Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, September 1–5, 1980

Sample text

This problem was selected as another test problem to compare the above sparse versions of the 3 stiff integrators. 4. Pre-ordering strategy was used in the sparse solver. 4. F4S appeared to be rather poor compared with the two other codes. 4. Computing times [s] required to solve Example 5 for 3 different accuracies GEARS GRKF4S METASl .. .... 85 11. 37 > 150. 15 .. . • ..... • I I I I I I II . . . II II • I II •• • II I I ' • I II II , • • • • .. 4. Sparse pattern of the Jacobian in Example 5 (NCR = 203, NSP = 55) version of DIFSUB (with numerical difference approximations for the Jacobian and no sparse solver): these simulations were a rough factor of 15 slower than the simulations with LARKIN.

10] and DAHLQUIST et al. 3). 12-16]. If, for example, gy is (everywhere) singular, we cannot expect to uniquely determine the limiting solution from the reduced problem alone. If gy has purely imaginary eigenvalues, we can expect rapidly oscillating solutions. If gy has eigenvalues with both posi- ° ° 21 tive and negative real parts, the boundary layer system is conditionally stable and we can expect nonuniform convergence (boundary layer behavior) for corresponding two-point problems at both endpoints.

Z o. o ... ~ (I. -. ' o u o. O. ,.......... --,-e'f2 D. Z D. -" TIME - E-2 Fig . 1 . Condensation of mesh points in the combustion zone of Example 1 (NCR =7, NSP=8). (. 17] the final concentration of water is lower than expected) all plots presented herein are obtained by interpolation over the set of those data points that have been automatically selected by the stepsize control-which is certainly much more economical, than prescribing equidistant data points in order to obtain a decent plot. 181) The chemical system is well described by the simpl ified so-called "Oregonator" model, which consists of NCR~5 reactions for NSP=5 species.

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