Stiff ODE solvers for detailed chemistry in CFD

Increasingly large chemical mechanisms are needed to accurately predict autoignition, heat release and pollutant emissions in computational fluid dynamics (CFD) simulations of in-cylinder processes in compression-ignition engines. Calculation of chemical source terms usually dominates the computational effort, and several strategies have been proposed to reduce the high computational cost associated with realistic chemistry in CFD. Central to many strategies is a stiff ODE solver to compute the change in composition due to chemical reactions over a computational time step. Most work to date on stiff ODE solvers for computational chemistry has focused on improving the efficiency of backward differentiation formula (BDF) methods for homogeneous systems, and has not explicitly considered the implications of how the stiff ODE solver couples with the CFD algorithm. In this work, a fresh look is taken at stiff ODE solvers that considers how the solver is integrated into a combustion CFD code, and the advantages of an alternative class of solvers (extrapolation methods) are demonstrated. Results for homogeneous systems and homogeneous-charge compression-ignition (HCCI) engines are presented for chemical mechanisms that range in size from fewer than 50 to more than 5000 species. Approximately linear scaling (linear increase in CPU time with increasing chemical mechanism size) is demonstrated, with the extrapolation solver being at least a factor of two faster than the BDF solver for mechanisms containing 100 or more species. The advantages of extrapolation methods are explained in terms of the operator-splitting strategies that are used for combustion CFD (where solver reinitialization is a key issue), and the range of relevant chemical time scales compared to the CFD time steps that are used in practice.