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Fractional step algorithm for solving a multi‐dimensional diffusion‐migration equation
Author(s) -
Kwok YueKuen,
Wu Charles C. K.
Publication year - 1995
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690110407
Subject(s) - constraint (computer aided design) , mathematics , diffusion , algorithm , diffusion equation , diffusion process , two step , order (exchange) , computer science , geometry , innovation diffusion , physics , thermodynamics , knowledge management , economy , finance , economics , service (business)
The earlier fractional step algorithm for solving the diffusion–migration equation in electrochemistry is extended to a multi‐dimensional multi‐species system with second‐order spatial accuracy. For each time‐step increment, the algorithm consists of three stages: (i) diffusion, (ii) satisfaction of the electroneutrality constraint, and (iii) migration. Each stage accounts for one individual physical process. Exact analytical solutions are derived for a two‐species system and comparisons between exact and numerical results are made. Numerical results are also obtained for a two‐dimensional three‐species electrochemical model. © 1995 John Wiley & Sons, Inc.