Combustion and Flame 155 (2008) 585–604 www.elsevier.com/locate/combustflame A graph-based approach to developing adaptive representations of complex reaction mechanisms Kaiyuan He, Marianthi G. Ierapetritou, Ioannis P. Androulakis ∗ Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA Received 9 January 2008; received in revised form 9 May 2008; accepted 12 May 2008 Available online 13 June 2008 Abstract An effective adaptive mechanism reduction approach based on flux graph clustering is proposed in this paper. The instantaneous element flux is quantified and considered as a proxy for describing the reactive propensities of the system. Our underlying hypothesis is that even though particular conditions may be characterized by a multitude of combinations of species mass fraction, T , and P , the essential chemistry, and hence the reaction propensity of the mixture that is active under this family of conditions, is the same. Therefore, we opt to use the instantaneous fluxes through the active reactions as an intrinsic property of the system. Flux graphs are first constructed for the chemical reaction system under numerous conditions aiming at capturing the attainable region. Similarity between flux graphs is quantified through the distances between corresponding vectors, using the cosine coefficient and a novel graph-distance metric taking into account the magnitude of each flux and the activity distribution of different fluxes. A hierarchical clustering algorithm is implemented to group similar instantaneous flux graphs into clusters, and consequently a reduced mechanism is generated for each cluster. A search algorithm is defined afterward to assign a new query point to a particular flux graph cluster, and subsequently the reduced mechanism associated with this cluster is used to describe the system at this time point. Finally, the methodology is demonstrated using n-pentane combustion in an adiabatic plug flow reactor model and a pairwise mixing stirred reactor model.  2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Flux graph; Graph clustering; Kinetic model; Adaptive reduction 1. Introduction Fuel combustion is a very active research field, and a number of detailed kinetic mechanisms have been developed to model a variety of chemical pro- cesses [1–7]. Many important applications, including * Corresponding author. Fax: +1 732 445 3753. E-mail address: yannis@rci.rutgers.edu (I.P. Androulakis). aerospace propulsion, car engine simulation and de- sign, and various manufacturing processes, require a detailed understanding of both fluid dynamics and ki- netics. However, detailed simulation of reactive flow systems using complex kinetic mechanisms consist- ing of hundreds of species and thousands of reactions is a computationally very demanding task. Hence considerable effort has been invested in the represen- tation of complex kinetic models by simpler, reduced models that can largely alleviate the computational complexity while still retaining considerable accu- 0010-2180/$ – see front matter  2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2008.05.004