A hybrid implicit-explicit time integration for stiff chemically reacting flows based on adaptive component-splitting method

Numerical simulations of chemically reacting flows often suffer from stiffness arising from the large disparities in time scales among advection, diffusion, and chemical reactions, which severely limits computational efficiency. To address this challenge, this study proposes a hybrid implicit-explicit component-splitting method that decomposes the governing equations into two subsystems: a flow subsystem handling advection-viscous terms through explicit time integration, and a component subsystem treating diffusion-reaction terms via implicit time integration. This framework effectively combines the accuracy of explicit methods with the efficiency and stability of implicit schemes. In regions exhibiting strong stiffness, the local time step of the component subsystem is adaptively reduced by an appropriately chosen divisor to improve numerical stability and robustness. Furthermore, a species-invariance criterion based on local mass-fraction gradients and reaction activity is incorporated to selectively update the component subsystem, thereby reducing redundant computations. For unsteady flows, the proposed method permits significantly larger time steps than explicit Runge-Kutta schemes, while for steady flows it increases the maximum stable Courant-Friedrichs-Lewy number and reduces time cost per iteration. Several test cases, including hydrogen-air detonations and hypersonic non-equilibrium flows, demonstrate the method's effectiveness: it maintains stability at large time steps, accurately captures the complex interactions between shock and detonation waves, and shows excellent agreement with high-order Runge-Kutta simulations. Overall, the proposed implicit-explicit method enables efficient, accurate, and robust simulations of chemically reacting flows with stiff chemistry.