pyJac: analytical Jacobian generator for chemical kinetics

Kyle E. Niemeyer, Nicholas J. Curtis, Chih-Jen Sung
School of Mechanical, Industrial, and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331, USA
arXiv:1605.03262 [physics.comp-ph], (11 May 2016)


   title={pyJac: analytical Jacobian generator for chemical kinetics},

   author={Niemeyer, Kyle E. and Curtis, Nicholas J. and Sung, Chih-Jen},






Accurate simulations of combustion phenomena require the use of detailed chemical kinetics in order to capture limit phenomena such as ignition and extinction as well as predict pollutant formation. However, the chemical kinetic models for hydrocarbon fuels of practical interest typically have large numbers of species and reactions and exhibit high levels of mathematical stiffness in the governing differential equations, particularly for larger fuel molecules. In order to integrate the stiff equations governing chemical kinetics, generally reactive-flow simulations rely on implicit algorithms that require frequent Jacobian matrix evaluations. Some in situ and a posteriori computational diagnostics methods also require accurate Jacobian matrices, including computational singular perturbation and chemical explosive mode analysis. Typically, finite differences numerically approximate these, but for larger chemical kinetic models this poses significant computational demands since the number of chemical source term evaluations scales with the square of species count. Furthermore, existing analytical Jacobian tools do not optimize evaluations or support emerging SIMD processors such as GPUs. Here we introduce pyJac, a Python-based open-source program that generates analytical Jacobian matrices for use in chemical kinetics modeling and analysis. As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation, then demonstrate the performance achievable on CPUs and GPUs using pyJac via matrix evaluation timing comparisons.
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