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TLM model of waves in moving media. (English) Zbl 0996.65091

Summary: Waves in moving media arise in fluid mechanics and elastic mechanics and are especially significant in acoustics. They are characterized by direction-dependent wave speeds. When compared with the wave equation, the governing differential equation, \(y_{tt}+\alpha y_{xt}+\beta y_{xx}= 0\) has an extra, cross derivative term. An original solution method based on transmission line matrix (TLM) modelling is presented. By means of supplementary link lines controlled by notional ‘diodes’ the TLM mesh wave propagation characteristics are directionally biased. The algorithm is derived and performance assessed for the one-dimensional case. Numerical results agree closely with analytical solutions. The algorithm has interesting properties promising new application areas for TLM.

MSC:

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

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