Implementation of α-QSS stiff integration methods for solving the detailed combustion chemistry

Implicit methods for reacting flow systems are considered efficient when expressed in terms of a time step length. A drawback of these methods is the additional work required at each time step for solving the sparse matrix of algebraic equations, which degrades their efficiency. Explicit methods are easy to implement but require excessively small steps. Predictor-corrector methods are another option, which utilise the concepts of both implicit and explicit methods. A recently proposed alpha-QSS (quasi steady state) method is an example of a second order predictor-corrector A-stable method. In the present study we carry out integration of a one dimensional laminar methane flame. During the integration of the methane mechanism the method requires small time steps where concentrations are rapidly varying. In the pre-heat and equilibration periods, the method is not efficient and unnecessarily takes smaller steps. An alteration is proposed in the convergence criteria which improves the efficiency of the method in the pre-heat and equilibration zones, and which results in a reduction in the computation time by a factor of 15. Due to the small time step, the temperature change at each step is also small, so an additional time saving can be achieved if rate coefficients are calculated only after a predetermined change in temperature. http://www.iaeng.org/publication/WCE2007/WCE2007_pp1352-1357.pdf