An Exponential Integrator with Schur–Krylov Approximation to accelerate combustion chemistry computation

Abstract

The Exponential Integrator with Schur–Krylov Approximation (EISKA) algorithm was developed for combustion applications. This algorithm combines the advantages of the explicit large step advancement of the exponential schemes and the dimension reduction effect of the Krylov subspace approximation, and was improved by introducing the Schur decomposition to control the rounding error. The EISKA based on the SpeedCHEM (SC) package was implemented to simulate a methane partially stirred reactor (PaSR) with pair-wise mixing model by considering the mechanisms of Li et al., GRI-Mech 3.0 and USC Mech II. Accuracy and computational efficiency of EISKA are systematically compared with those of DVODE. In the case of the Li mechanism which is a priori sufficiently small to be handled directly in combustion simulations, the computations were accelerated by a factor of 1.99 without losing accuracy. In the cases of GRI-Mech 3.0 and USC Mech II which are significantly larger than the Li mechanism, chemical reduction methods, namely the Correlated Dynamic Adaptive Chemistry (CoDAC) and the Multi-timescale (MTS) method were coupled with either DVODE or EISKA. The results show that the EISKA is faster than DVODE either with or without chemical reduction methods. Model results show that the best strategy is to use EISKA without any reduction method which leads to the same accuracy as compared to DVODE and acceleration factors of 2.61 and 2.19 for GRI-Mech 3.0 and USC Mech II, respectively.