Stability of the totally implicit finite difference scheme for the one-dimensional diffusion equation with a moving boundary |
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Authors: | Dr. M. Fabbri |
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Affiliation: | 1. Laboratório Associado de Sensores e Materiais-LAS, Instituto de Pesquisas Espaciais-INPE, Caixa Postal 515, 12201, S?o José dos Campos, SP, Brazil
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Abstract: | We analyze the totally implicitO(h 2 k) finite difference method applied to a linear unidimensional diffusion equation with a boundary moving with constant velocity. The related physical problem is the solidification of a finite column filled with a binary mixture, in the quasiequilibrium regime. By advancing the boundary along the pathh/k=velocity of the interface, a simple algorithm is obtained which is shown to be consistent and unconditionally stable for any value of the interfacial segregation factor and of the Peclet number. |
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