A STATE REUSE RADAU FRAMEWORK FOR ACCELERATING COMBUSTION REACTION KINETICS

To reduce the high cost of Jacobian construction and linear-system factorization in stiff ordinary differential equation integration for combustion reaction kinetics, a state-reuse accelerated solver, named State Reuse Radau (SR-Radau), was developed based on a fixed fifth-order Radau IIA method. The purpose of the method is to lower computational cost without changing the original discretization formula or order properties of Radau IIA. In the simplified Newton iteration, thermochemical-state similarity is introduced to judge whether a cached Jacobian can still be used. The decision is based on variations in thermochemical state between adjacent accepted steps, and the cache information is updated and screened along the accepted-step sequence. For low-concentration species with variations across several orders of magnitude and for strongly nonlinear ignition stages, cache-quality checks, Jacobian recomputation, pre-integration diagnosis, and fallback treatment are further designed. These treatments are used to restrict the continued reuse of low-quality cached Jacobians, so that cached Jacobians are mainly reused in intervals where the thermochemical states are close and the Newton iteration remains stable. When the pre-integration diagnosis indicates a high reuse risk, the computation is switched to a more robust integration route. Four combustion mechanisms covering different fuel types and mechanism sizes were tested at 1200 K, 1400 K, and 1600 K under the same constant-pressure adiabatic zero-dimensional ignition model to evaluate the proposed method. The representative variables include temperature, fuel, major products, and key radicals, and numerical accuracy is assessed using trajectory and ignition-delay errors. The results show that, except for one low-temperature boundary case, SR-Radau achieves acceleration in 11 cases satisfying the error constraints, with speedups from 1.15 to 6.80. Representative-variable trajectories, error metrics, and computational-cost indicators, including function evaluations, Jacobian evaluations, and lower-upper (LU) factorizations recorded during the solver runs, show that the method reduces the cost of Jacobian construction and linear-system factorization while maintaining the consistency of the main physical trajectories. The pre-integration diagnosis can identify reuse risks and switch to a more robust solver when necessary.