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A transmission line modelling (TLM) method for steady‐state convection–diffusion
Author(s) -
Kennedy Alan,
O'Connor William J.
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2049
Subject(s) - convection–diffusion equation , steady state (chemistry) , diffusion , convection , diffusion equation , péclet number , transmission line , mathematics , telegrapher's equations , mathematical analysis , mechanics , physics , computer science , thermodynamics , chemistry , engineering , operations management , metric (unit) , telecommunications
This paper describes how the lossy transmission line modelling (TLM) method for diffusion can be extended to solve the convection–diffusion equation. The method is based on the correspondence between the convection–diffusion equation and the equation for the voltage on a lossy transmission line with properties varying exponentially over space. It is unconditionally stable and converges rapidly to highly accurate steady‐state solutions for a wide range of Peclet numbers from low to high. The method solves the non‐conservative form of the convection–diffusion equation but it is shown how it can be modified to solve the conservative form. Under transient conditions the TLM scheme exhibits significant numerical diffusion and numerical convection leading to poor accuracy, but both these errors go to zero as a solution approaches steady state. Copyright © 2007 John Wiley & Sons, Ltd.