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Wave speeds for a TLM model of moving media. (English) Zbl 0996.65090

Summary: In a companion paper [ibid. 15, No. 2, 205-214 (2002; reviewed below)] a transmission line matrix (TLM) scheme is presented for the solution of the 1-D equation of waves in moving media, \(y_{tt}+ \alpha y_{xt}+ \beta y_{xx}= 0\), 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.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations

Citations:

Zbl 0996.65091
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References:

[1] O’Connor, International Journal of Numerical Modelling 15 pp 205– (2002) · Zbl 0996.65091
[2] Linear and Nonlinear Waves, Wiley: New York, 1974.
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