An explicit numerical scheme for homogeneous gas-phase high-temperature combustion systems

Abstract

We introduce a new and very simple explicit numerical method for a system of stiff ordinary differential equations (ODEs) that arises from combustion. The main aim of this paper is to show that, contrary to popular belief, an almost trivial explicit method can solve a small class of large nontrivial stiff systems surprisingly efficiently. The algorithm, which is motivated by the theory of Markov jump processes, is very simple and easy to implement. Various numerical experiments are performed to assess the efficiency of the algorithm. For this the ignition of a stoichiometric mixture of n-decane and air at constant pressure and temperature is calculated using a mechanism containing 1218 species and 4825 reactions. For the considered system at moderate accuracy requirements, the new algorithm exhibits performance several orders of magnitude better than standard explicit methods and in the same order of magnitude as the implicit solver packages DASSL and LSODE. The numerical experiments also indicate that the approximate solution obtained from the new algorithm converges to the exact solution of the ODE. Furthermore, we address limitations of our numerical scheme, such as its restriction to the high-temperature regime and moderate accuracy.