A semi-implicit method for the finite-rate chemistry integration in numerical simulations of combustion: Application to highly compressible flows

Combustion simulations with detailed chemical kinetics are computationally demanding due to the stiffness of the equations involved. While explicit integration methods are limited by stability constraints requiring very small time steps, semi-implicit approaches offer more efficient alternatives. An improved version of the semi-implicit scheme ODEPIM, ODEPIM ⋆ , is proposed and validated for compressible flows. It dynamically adapts the chemical sub-time step based on locally rate-limiting species and uses production/consumption rates to ensure stability. The method also simplifies temperature integration. ODEPIM ⋆ achieves up to 20 × speed-up in kerosene combustion cases compared to explicit solvers, without sacrificing accuracy. Its effectiveness is further demonstrated in a realistic cavity-based scramjet simulation with transverse hydrogen injection, where it accurately captures key flame stabilization mechanisms. The results closely match both explicit simulations and experimental data, confirming the method’s reliability and efficiency for detailed chemical kinetics integration.