Speedy solution of quasi-steady-state species by combination of fixed-point iteration and matrix inversion

A speedy algorithm that utilizes both fixed-point iteration (FPI) and matrix inversion is developed for solving a set of nonlinear, coupled algebraic equations for the concentrations of the quasi-steady state (QSS) species in reduced mechanisms. It is shown that the slow convergence of FPI experienced in some reduced mechanisms is caused by QSS species that are strongly coupled. A method is developed for identifying groups of QSS species that are coupled and closely connected. During the iteration, the concentrations of those species without coupling to other species are obtained by FPI. The concentrations of species in coupled groups are solved by matrix inversion as FPI is inefficient. Using three reduced mechanisms with total number of QSS species ranging from 17 to 251, the performances of the proposed algorithm are extensively assessed. It is concluded that the proposed algorithm offers significant CPU savings when the coupling among species is strong.