NUMERICAL STUDY OF THE INTERACTION OF FAST CHEMISTRY AND DIFFUSION

A model problem that contains the essential features of most combustion processes has been formulated and used to characterize the efficiency of five numerical solution procedures. Chemistry is modeled by both one- and two-step Arrhenius-type reactions, which allows the effect of stiffness on the efficiency of the methods to be assessed parametrically. The numerical schemes evaluated include two methods of lines techniques, two schemes which use pointwise integration of reaction terms in conjunction with different diffusion models, and a locally linearized block tridiagonal, implicit procedure. The latter technique with fourth-order 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 to two-dimensional problems of combustion in a gaseous medium are discussed qualitatively. © 1979 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.