Use of a dynamic network for the TLM solution of diffusion problems

Abstract

There is a class of material processing simulators which require solution of the diffusion equation over a surface which is evolving due to some physical or chemical process related to the concentration of the diffusing species. Because of its explicit and unconditionally stable nature, the transmission line matrix (TLM) method is well suited to efficiently solve the diffusion equation in these instances. However, the methodology for using TLM on a dynamic problem space is not well established. This paper describes the development of algorithms to handle the insertion, deletion and motion of TLM nodes along the one-dimensional surface of a two-dimensional thin film process simulator called GROFILMS. These routines are completely compatible with concurrent time scaling to increase computational efficiency. Central to this development is the use of an asymmetric TLM cell which provides more flexibility for representation and minimizes the disturbance effects of these nodal operations. The scaling routines apply conservation of charge and continuity of current into the affected region to recompute the scattered or the incident pulses as a result of the evolving network. Verification of these results through comparison with known analytic solutions is achieved where possible. © 1998 John Wiley & Sons, Ltd.