A dynamic adaptive method for hybrid integration of stiff chemistry

The operator-splitting schemes for integration of stiff diffusion–reaction systems were found to fail in error control, i.e. incurring O(1) relative errors, with splitting time steps larger than that required for fully explicit integration, when significant non-chemical radical sources are present. It was shown that, by excluding the transport term from the chemistry integration, errors by orders of magnitude may occur in radical concentrations solved in the chemistry sub-step, resulting in significant errors in the major species. The failing scenario is demonstrated with a toy problem and an unsteady perfectly-stirred reactor (PSR) for hydrogen/air with significant H radical concentration at inlet. A dynamic adaptive method for hybrid integration (AHI) of stiff chemistry is then proposed as a substitute for the operator-splitting schemes in such cases. The AHI method can obtain accurate solutions by integrating the fast species and reactions implicitly and the non-stiff terms, including slow reactions and non-chemical source terms, explicitly. Specifically, fast species and reactions are identified on-the-fly based on their analytically derived timescales, the rates of slow variables are evaluated explicitly and those of fast species are evaluated partial-implicitly. As such, the number of variables to be implicitly solved at each integration time step is reduced to the number of the fast species, resulting in a smaller Jacobian matrix and consequently lower computational cost compared with the fully implicit solvers. The hybrid method is validated in auto-ignition for hydrogen/air with different equivalence ratios and initial temperatures, and compared with the Strang splitting scheme for the toy problem and the unsteady PSR. Results show significant improvement in accuracy using the AHI method.