Generalized preconditioning for accelerating simulations with large kinetic models

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Detailed modeling of the combustion of real transportation fuels and the atmospheric reactions involving their emissions is prohibitively expensive, due to the large size and stiffness of the chemical kinetic models. Adaptive preconditioning is a method used to reduce the cost of integrating large kinetic models by forming a preconditioner based on a semi-analytical Jacobian matrix, paired with sparse linear algebra procedures. In this study, we extend this preconditioning method to a more-general mole-based state vector formulation applicable to generic reactor types and combinations. We tested the scheme using constant-pressure and constant-volume ideal-gas reactor simulations, showing speedup in performance from a factor of 3 up to nearly 4000 times for chemical kinetic models with 10 to 7171 species, in comparison with typical dense solvers. The method also improves performance by a factor of 1.06 to 21.1, for models larger than 200 species, in comparison with a fully exact, analytical Jacobian used as the preconditioner. Overall, this method improves performance by up to three orders of magnitude for large kinetic models, and offers benefits for models with as few as 10 species.