An Efficient Multi Time Scale Method for Solving Stiff ODEs with Detailed Kinetic Mechanisms and Multi Scale Physical Chemical Processes

Abstract

In direct numerical simulations of reactive flow and other multi scale physical problems, a broad time scale distribution from seconds to a fraction of nano-seconds makes explicit schemes in-efficient. On the other hand, although implicit methods may improve computational efficiency, they lose the time histories and statistical values of the fast modes, which may be required for modeling of large scale slow modes in a turbulent reactive flow and multi physical process. In the present study, a dynamic multi time scale (MTS) method and a dynamic hybrid multi time scale (HMTS) model are developed to achieve efficient and time accurate integration of stiff ODEs with detailed kinetic mechanisms. The methods are applied to ignition of hydrogen, methane and n-decane/air mixtures and compared, respectively, with standard Euler and implicit ODE solvers by using detailed chemical kinetic mechanisms. The results showed that both methods can accurately reproduce the species time histories and ignition delay times. In addition, compared to the explicit Euler method, MTS is not only computationally efficient but also robust at larger time steps. Compared to the implicit ODE solver, MTS is about one-order more computationally efficient. In addition, unlike the implicit ODE solver, whose computation time is proportional to the square of the species number, the computation time required for MTS is only proportional linearly to the species number. As such, MTS has advantages particularly for large equation systems such as large chemical kinetic mechanisms. To further accommodate the specification of a limiting time scale of the equation system and to improve the computation efficiency and robustness at large time scales, HMTS is developed by integrating MTS with a fully implicit algorithm. Therefore, the present HMTS is a generalized scheme which includes the Euler scheme, MTS, and implicit scheme, and compatible to both incompressible and compressible flow solvers. The results showed HMTS is rigorous and efficient. This scheme can be used for direct numerical simulations and large eddy simulation with detailed chemical mechanisms to improve the computation efficiency, accuracy, and robustness.