Solutions of diffusion equations by Fourier expansions

Abstract

One- and two-dimensional diffusion equations in slab geometry are solved by a method of Fourier expansion. In this method, at first, equations for the fluxes on the boundaries and their normal derivatives are derived. Applying boundary conditions, these equations are solved and all boundary values are determined. Then using these boundary values, the Fourier coefficients of the flux in the region are calculated. Different from the eigenfunction expansion method, the function series used for the expansion is independent of the boundary conditions. Therefore multi-regional problems are also solved by this method. The results of the numerical calculations are given and compared with the results by the usual finite difference method.