TLM for diffusion: consistent first time step. Two-dimensional case

✍ Scribed by Peter Enders; Susan H. Pulko; David M. Stubbs

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 107 KB
• Volume: 15
• Category: Article
• ISSN: 0894-3370
• DOI: 10.1002/jnm.440

✦ Synopsis

Abstract

In initializing a transmission line matrix (TLM) diffusion model it is necessary to consider both initial concentration (temperature) and initial flow. As usual, only one of them is given; an auxiliary formula is necessary to calculate the distribution for the first time step. It has been shown that the standard formula may introduce additional numerical errors (International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 1993; 6:135; International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 1993; 6:161) and that these errors can persist over many time steps. In this paper, we show how an initial modification to the normal TLM algorithm can remove such errors, and we demonstrate the method by applying it to a two‐dimensional TLM heat diffusion model for a copper plate. Copyright © 2002 John Wiley & Sons, Ltd.