Numerical Study of the Interaction of Fast Chemistry and Diffusion

A model problem which contains the essential features of most combustion processes has been formulated and is used to characterize the efficiency of five numerical solution procedures. Chemistry is modeled by both one and two-step Arrhenius-type reactions which allow the effect of stiffness on the efficiency of the methods to be parametrically assessed. The numerical schemes evaluated include two method of lines techniques, two methods that integrate reaction terms point-by-point, and a linearized block tridiagonal, implicit procedure. The latter technique with fourth order Pade' spatial differences has been found to be most efficient over a wide range of reaction rates including cases with considerable stiffness. Combination of this method with adaptive gridding schemes and extension of the method to two-dimensional problems of combustion in a gaseous medium are discussed qualitatively.