Efficient time stepping for reactive turbulent simulations with stiff chemistry

摘要

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 advection-diffusion and reaction operators are decoupled using the simpler balanced splitting method, which is constructed with improved stability properties and reduced computational cost. The method is shown to achieve stable and accurate prediction of ignition and extinction for reaction-diffusion systems near critical conditions. A ROK4E scheme is developed 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 only three right-hand-side evaluations over four stages. Combing these two methods, efficient calculations are achieved for large-scale parallel simulations of turbulent flames.