Time integration of chemical kinetics with computational singular perturbation and tabulation

Computational Singular Perturbation (CSP) allows the identification and removal of fast time scales in stiff chemical kinetic systems, thereby enabling time integration with explicit time stepping algorithms along slow invariant manifolds in the system. In this paper, we develop a tabulation method to improve the efficiency of the CSP integration approach by allowing re-use of previously computed CSP information. To enable flexible, adaptive, and efficient tabulation in chemical systems with high-dimensional state spaces, the method relies on nearest neighbor searches in kd-tree data structures. As the CSP information only depends on the current number of active modes in the system, tables can be constructed in a reduced-dimensional space, with increased efficiency as the number of exhausted modes increases. The approach is demonstrated on the simulation of hydrogen-air autoignition.