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A MODIFIED FINITE DIFFERENCE METHOD FOR MODELLING DIFFUSION PROCESSES
Author(s) -
ZHANG H. X.,
WEBB P. W.
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(199605)9:3<215::aid-jnm220>3.0.co;2-r
Subject(s) - finite difference method , finite difference , transient (computer programming) , diffusion , finite element method , transmission line , matrix (chemical analysis) , computer science , mathematics , diffusion equation , mathematical analysis , physics , engineering , materials science , telecommunications , metric (unit) , operations management , composite material , thermodynamics , operating system
A time domain unconditionally stable explicit method is presented which may be used to model processes governed by the diffusion equation such as transient heat flow. Unlike the explicit finite difference routine, the method models the diffusion process within the time step (MPWT). Being explicit, the method (MPWT) may easily account for non‐linear physical parmeters and may be compared with the transmission line matrix (TLM) method of diffusion modelling in terms of its utility. Unlike the TLM model, however, the equivalent circuit does not contain inductive components which have no clear physical meaning. The MPWT method is based on a simple resistive and capacitive circuit model, which for short time steps reduces to the explicit finite difference formulation but is stable for large time steps. Good agreement has been found when results obtained using this algorithm are compared with other numerical methods and analytical results.