Boundary conditions in TLM diffusion modelling

Abstract

SUMMARYThe connection algorithms used in transmission-line matrix (TLM) modelling of diffusion processes for describing boundary conditions in both link-line and link-resistor nodal configurations have been derived. The new algorithms regarding the inhomogeneous Robin condition enhance the capability of the TLM method in simulating thermal or particle diffusion phenomena. A number of boundary treatments in the existing literature have been found to be special cases of our results. The Dirichlet-type boundary condition is also discussed. TLM numerical results using the new algorithms, particularly with the link-resistor model for achieving signal synchronization, are shown to be in excellent agreement with the available analytical solutions.