A Low-Computational-Cost Strategy to Localize Points in the Slow Manifold Proximity for Isothermal Chemical Kinetics

Abstract

Dimensionality reduction for the modeling of reacting chemical systems can represent a fundamental achievement both for a clear understanding of the complex mechanisms under study and also for the practical calculation of quantities of interest. To tackle the problem, different approaches have been proposed in the literature. Among them, particular attention has been devoted to the exploitation of the so-called slow manifolds (SMs). These are lower dimensional hypersurfaces where the slow part of the evolution takes place. In this study, we present a low-computational-cost algorithm (based on a previously developed theoretical framework) for the localization of candidate points in the proximity of the SM. A parallel implementation (called DRIMAK) of such an approach has been developed, and the source code is made freely available. We tested the performance of the code on two model schemes for hydrogen combustion, being able to localize points that fall very close to the perceived SM with limited computational effort. The method can provide starting points for other more accurate but computationally demanding strategies; this can be a great help especially when no information about the SM is available a priori, and very many species are involved in the reaction mechanism.