Wave speeds for a TLM model of moving media

In a companion paper, a transmission line matrix (TLM) scheme was presented for the solution of the 1-D equation of waves in moving media, y_tt+αy_xt+βy_xx=0, describing the superposition of two waves with direction-dependent speeds. The TLM model achieved controlled, direction-dependent wave-speed bias by means of supplementary link lines with notional ‘diodes’. Expressions for wave speed, presented without proof, were verified. Here a proof is presented using a new, time-domain approach. The apparent (direction-dependent) inductance and capacitance as seen by a single wave are first established in a generalized way from the TLM algorithm, from which two wave speeds and impedances are then derived. Copyright © 2002 John Wiley & Sons, Ltd.