Solutions of diffusion equations by Fourier expansions

Nobuo Ohtani, Jungchung Jung, Keisuke Kobayashi, Hiroshi Nishihara
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引用次数: 6

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.

扩散方程的傅里叶展开解
用傅里叶展开法求解了平板几何中的一维和二维扩散方程。该方法首先导出了边界上的通量及其法向导数的方程。应用边界条件对这些方程进行了求解,并确定了所有的边界值。然后利用这些边界值计算区域内通量的傅里叶系数。与特征函数展开法不同的是,用于展开的函数级数与边界条件无关。因此,该方法也可以解决多区域问题。给出了数值计算结果,并与常用的有限差分法计算结果进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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