A species-clustered splitting scheme for the integration of large-scale chemical kinetics using detailed mechanisms

In this study, a species-clustered integrator for chemical kinetics with large detailed mechanisms based on operator-splitting is presented. The ordinary differential equation (ODE) system of large-scale chemical kinetics is split into clusters of species by using graph partition methods which have been intensely studied in areas of model reduction, parameterization and coarse-graining, e.g., diffusion maps based on the concept of Markov random walk. The definition of the weight (similarity) matrix is application-dependent and follows from chemical kinetics. Each species cluster is integrated by the variable-coefficient ODE solver VODE. The theoretically expected speedup in computational efficiency is reproduced by numerical experiments on three zero-dimensional (0D) auto-ignition problems, considering detailed hydrocarbon/air combustion mechanisms at varying scales, from 53 species with 325 reactions of methane to 2115 species with 8157 reactions of n-hexadecane. Optimal clustering weighing both prediction accuracy (for ignition delay and equilibrium temperature) and computational efficiency is implied with the clustering number N=2 for the 53-species methane mechanism, N=4 for the 561-species n-heptane mechanism and N=8 for the 2115-species n-hexadecane mechanism.