  A combination of a steady-state preserving operator splitting method and a
semi-implicit integration scheme is proposed for efficient time stepping in
simulations of unsteady reacting flows, such as turbulent flames, using
detailed chemical kinetic mechanisms. The operator splitting is based on the
Simpler balanced splitting method, which is constructed with improved stability
properties and reduced computational cost. The method is shown to be capable of
stable and accurate prediction of ignition and extinction for
reaction-diffusion systems near critical conditions. The ROK4E scheme is
designed for semi-implicit integration of spatially independent chemically
reacting systems. Being a Rosenbrock-Krylov method, ROK4E utilizes the low-rank
approximation of the Jacobian to reduce the cost for integrating the system of
ODEs that have relative few stiff components. The efficiency of the scheme is
further improved via the careful choice of coefficients to require three
right-hand-side evaluations over four stages. Combing these two methods,
efficient calculation is achieved for large-scale parallel simulations of
turbulent flames.
