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Мodeling of the surface-reaction diffusion and numerical solution

V. S. Zverev

Ural State University

Abstract: In this work process of surface-reaction diffusion is considered and mathematical model is suggested. It is a system of the partial derivative equations complicated unknown moving boundary. The given model is studied analytically and numerically. On the basis of the experimental facts the estimation of characteristic times is obtained. This makes it possible to simplify an initial problem and to build the approximate analytical solution. Using the method of final differences and the method of straightening of front, a algorithm of the numerical solution of the initial problem is constructed. Comparison of the numerical and analytical solution shows although there is a divergence in the process description at the initial stage, but both solutions equally transfer feature of the model with the course of time.

Keywords: surface diffusion, system of parabolic equations, moving boundary, asymptotic solution, finite difference method.

UDC: 517.958+544.034.54

Received: 29.09.2009

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