On solving the stiff ODE's of the kinetics of chemically reacting gas flow

We study the efficiency of computational methods for the stiff ordinary differential equations of chemical kinetics that arise when the partial differential equations of chemically reacting gas flow are treated by a fractional step technique. In this application, the overhead work associated with evaluating partial derivatives and decomposing matrices for the Newton-; like corrector iterations used in most algorithms for stiff ODE's can be eliminated for the most part by keeping in store a small number of suitably- chosen copies of the Jacobian matrix, reduced to Hessenberg form to facilitate changes of stepsize and order. Computational results in the case of ignition and propagation of a one-dimensional, premixed laminar flame with different realistic chemical kinetic models are presented to show the reduction of computational work obtained by modifying a modern general-purpose ODE-code in this manner.