Application of an explicit numerical method to a reaction-diffusion system in combustion

Abstract

Numerical methods are applied to one-dimensional unsteady reaction-diffusion equations to seek propagating wave solutions. These equations describe flame propagation in certain combustion systems. It is shown that the steady flame speed is invariant under this coordinate transformation. Model reaction-diffusion equations which admit traveling waves as exact solutions are formulated and one of these is solved. The diffusion terms are differenced using the explicit methods introduced by Saul'yev. Both implicit and explicit techniques for the reaction rate terms are tested. Results indicate that numerical diffusion can reduce accuracy significantly, that numerical dispersion truncation errors can reduce accuracy if they are sufficiently large, and that an accurate representation of the reaction rate in the difference equations is important to retain overall accuracy. One of the explicit methods is also applied to an ozone decomposition flame computation. An adaptive grid procedure is also implemented. Results show good agreement with the fourth order accurate results of Margolis.