Transmission-line matrix models for solving transient problems of diffusion with recombination

Starting from the general telegrapher's equation, we investigate two nodal network constructions for modelling diffusion with recombination by means of the transmission-line matrix (TLM) method. The diffusion effect is modelled by the series and shunt capacitance in one approach, and by the series inductance and shunt resistance in the other. Both approaches use the series and shunt resistances to model the recombination effect. The constraint of using both TLM networks for solving transient problems of diffusion with recombination is found to be identical in terms of the physics behind the numerical routines. A practical way of determining the spatial resolution and iteration time step for accurate TLM numerical computations is suggested based on a simple frequency analysis.