On a numerical relaxation method for a chemical reaction-diffusion problem with an instantaneous and irreversible reaction

摘要

in this paper we deal with a numerical method for a free boundary value problem in 1D, describing a chemical diffusion problem accompanied by an irreversible and instantaneous reaction which gives rise to a moving internal boundary. Basically, the method consists of four steps: (1) a Landau transformation mapping each of the 2 time varying intervals on a fixed domain, which results in a strongly nonlinear boundary value problem; (2) a central difference method with respect to the space variable, that takes properly into account the various transition conditions; (3) the construction of an ODE containing a relaxation parameter a to represent the movement of the internal boundary; (4) a time integration of the resulting stiff system of ODES by suitable computer packages. The numerical method is evaluated by comparison with an analytical solution for a special but nontrivial case, and by a mass-balance argument. The presented method can be extended to the case of several irreversible and instantaneous reactions. (C) 2003 Elsevier Ltd. All rights reserved. [References: 13]