Computations of laminar flame propagation using an explicit numerical method

Abstract

Numerical methods are applied to a coupled system of one-dimensional unsteady reactiondiffusion equations to seek propagating wave solutions. These equations model flame propagation in certain combustion systems when constant pressure combustion is assumed, with Lewis number unity, and when a Lagrangian coordinate transformation is introduced. In the numerical integration schemes the reaction terms are computed non-iteratively, using two different second-order accurate methods. In the first, the numerical timestep is limited by the Lipschitz timestep constraint as is the case with standard explicit schemes. The second scheme, is constructed in such a way that this timestep limitation is not present and computations are made with timesteps which are orders of magnitude larger than those possible with standard methods. In both schemes the diffusion terms are differenced using the unconditionally stable first order accurate explicit method introduced by Saul'yev. The leading truncation error of this method is a numerical dispersion error which has been found to reduce accuracy less than the numerical diffusion error which arises in more standard explicit methods. These numerical schemes are applied to an ozone decomposition flame model problem. An adaptive grid procedure is also implemented for further increases in computational efficiency and the results show good agreement with the fourth order accurate results of Margolis. This indicates that efficient lower order numerical methods can be sufficiently accurate for practical computations of combustion.