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TLM TREATMENT OF A GENERAL DIFFUSION FLUX BOUNDARY CONDITION
Author(s) -
GUI XIANG,
DEW STEVEN K.,
BRETT MICHAEL J.
Publication year - 1996
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/(sici)1099-1204(199609)9:5<327::aid-jnm238>3.0.co;2-b
Subject(s) - boundary (topology) , boundary value problem , diffusion , mathematical analysis , effective diffusion coefficient , mathematics , mechanics , physics , thermodynamics , medicine , radiology , magnetic resonance imaging
An approach of using a current‐controlled voltage source analogy to account for a general boundary condition of particle or thermal flux in transmission‐line matrix (TLM) diffusion modelling has been developed. For mass diffusion, this boundary condition is expressed as D ∂ C /∂ x + α C = 0, where C is the concentration, D is the diffusion coefficient, and α is a parameter characterizing the out‐diffusion mobility across the boundary of interest. Confirmation of the TLM numerical treatment through comparison with analytical solutions is presented. Besides the open‐circuit and short‐circuit boundaries, the matched‐load boundary is also found to be a special case of the present boundary condition. This extension of the boundary treatment allows the highly flexible TLM method to be applied to a greater variety of diffusion problems.