Novel reduction schemes for a dissipative dynamical system: A study on slow invariant manifolds in chemical kinetics

Abstract

This research explores the intricate concept of the Slow Invariant Manifold (SIM) and its pivotal role in developing model reduction techniques (MRTs) for challenges within dissipative systems in chemical kinetics, specifically in mechanical engineering. Focusing on the multi-step mechanism with two intermediates, primary approximations of the SIM are constructed and compared using two prominent MRTs: The Spectral Quasi Equilibrium Manifold (SQEM) and Intrinsic Low Dimensional Manifold (ILDM). At the given rate coefficient, a special computational experiment was performed in which the efficiency of chemical species has been compared. Noteworthy innovation involves evaluating SIM separately for reduced species, departing from the conventional approach of considering every species within the mechanism. The study employs local sensitivity analysis with MATLAB's Sim-Biology toolbox, presenting quantitative findings in a tabular format for a comprehensive MRT comparison. Beyond contributing to a deeper understanding of model reduction techniques in complex chemical kinetics, this research marks the first computational exploration of dissipative systems. The novel perspective of evaluating SIM for reduced species offers nuanced insights, emphasizing the critical role of SIM in effectively addressing challenges in mechanical engineering applications. In summary, this study introduces computational advancements and novel approaches, advancing model reduction techniques and highlighting the significance of SIM in addressing challenges within mechanical engineering contexts.