Applicability of the Homotopy Method to the determination of fixed points in chemical kinetics models

Reducing the complex chemical kinetics is an important challenge to impleme nt chemical schemes in a turbulent combustion code. An important step in th e reduction of chemical kinetics is to extract the fixed points of the set of differential equations associated with the chemical scheme since they ar e useful to determine the low manifolds which may be used to reduce kinetic mechanisms. This paper aims at testing a potentially powerful method, name ly the Homotopy Method, for extracting fixed points from nonlinear dynamica l systems. The method is tested on a 3D and a 7D model of the well-known Be lousov-Zhabotinskii reaction. This study shows that the Homotopy Method has a significantly better efficiency than available Newton-Raphson algorithms but that the stiffness of the chemical kinetics equations still resists th is method when the number of species increases. (C) 2000 Elsevier Science I nc. All rights reserved.