Numerical Treatment of Chemical Rate Networks for the Modelling of Oxygenrich Stellar Envelopes

Johannes Kaiser

Diplomarbeit, Technische Universität Berlin, 1996

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Abstract:

My Diplomarbeit at the Technische Universität Berlin is written in German. It has the title: Numerische Behandlung chemischer Ratennetzwerke für die Modellierung sauerstoffreicher stellarer Umgebungen.

It is intended to use reduced/simplified chemical reaction rate networks in selfconsistent numerical models of circumstellar envelopes (CSEs) for the description of chemical non-equilibrium effects. To automatically analyse and reduce/simplify chemical reaction rate networks, I tested an algorithm suggested by Lam und Goussis for reducing the stiffness of ordinary differential equations. This algorithm is based on an eigenvalue analysis of the Jacobian matrix of the rate vector with respect to the species concentrations.

I tested an implementation (in Fortran77) by the authors, found imcompatibilities with existing simulation programs for CSEs and implemented the algorithm myself (in C++) with a clearly defined interface to overcome these incompatibilities.

The program is working correctly. However, it is (still) too slow when many, say 100, species are included in the computation. It is also too slow when the interval of integration is very large and additionally the physical conditions, i.e. temperature and density, vary slowly. Therefore, I pointed out some means for further optimisation of the execution speed of my implementation.

The algorithm was named computational singular perturbation by the authors and put forth, e.g. in: Lam, S.H. und Goussis, D.A., 1991. Conventional asymptotics and computational singular perturbation for simplified kinetics modelling. In Smooke, M.D., Editor, 1991. Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames. Lecture Notes in Physics. Springer-Verlag, Berlin, Heidelberg.