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TLM nodal state estimator: An alternative method of initializing a two‐dimensional diffusion model
Author(s) -
Koay A. L.,
Wilkinson A. J.,
Pulko S. H.
Publication year - 2008
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/jnm.677
Subject(s) - initialization , boundary value problem , estimator , diffusion , boundary (topology) , matrix (chemical analysis) , computer science , line (geometry) , thermal , mathematics , mathematical analysis , physics , geometry , materials science , thermodynamics , statistics , composite material , programming language
The transmission line matrix (TLM) method is an established technique for modelling thermal transients in heat transfer systems. However, initial and boundary conditions have always been slightly problematic, particularly when the boundary condition is specified as a temperature ( Transmission Line Matrix ( TLM ) Techniques for Diffusion Applications . Gordon & Breach: London, 1998), for example, when the body of interest is suddenly exposed to a different temperature on its surface. In such a case the modelled solution contains additional dynamics that are associated with the two sub‐meshes in the TLM network and the two timesteps necessary for the temperature change to be fully communicated. These initialization problems are related to the fact that the boundary temperature in merely imposed as a fixed value on the network; the fundamental information‐carrying quantity, on the other hand, is the pulse, the thermal state of the body being represented by the distribution of pulses. Here, we aim to provide an alternative initialization approach, using nodal state estimation to derive pulse distributions from boundary and initial conditions specified by temperature. Consideration is given to the accuracy of the estimator by comparison with the first timestep solution proposed by Enders ( Int. J. Numer. Model . 2002; 15 :251–259). Copyright © 2008 John Wiley & Sons, Ltd.