Efficient time-stepping techniques for simulating turbulent reactive flows with stiff chemistry

In this work, a set of techniques is developed for the efficient temporal integration of compressible turbulent reacting flows with stiff chemistry. The proposed approach combines steady-state preserving operator splitting, semi-implicit ODE integration, and dynamic load rebalancing. Specifically, the simpler balanced splitting method is constructed as a second-order steady-state preserving operator splitting formulation, with improved stability properties and reduced computational cost compared with the original simple balanced splitting method. The method is shown to be capable of accurately capturing ignition and extinction for reaction–diffusion systems near critical conditions. The semi-implicit integration scheme, namely ROK4E, is constructed following the order conditions of the Rosenbrock–Krylov methods with improved efficiency. Designed for the integration of homogeneous reacting systems, ROK4E utilizes the low-rank approximation of the Jacobian to reduce the cost for integrating the system of ODEs that has relatively few stiff components compared with the interval of the integration. To address the scalability issue associated with the spatial clustering of chemical reactivity, a dynamic load rebalancing procedure is developed. The resulting time-integration techniques are employed in a 3D simulation of a temporally evolving turbulent planar flame with dimethyl ether/air chemistry, and improvements with respect to the computational efficiency and strong scalability are examined.