Diffusive representations for the analysis and simulation of flared acoustic pipes with visco-thermal losses

Abstract : Acoustic waves travelling in axisymmetric pipes with visco-thermal losses at the wall obey a Webster–Lokshin model. Their simulation may be achieved by concatenating scattering matrices of elementary transfer functions associated with nearly constant parameters (e.g. curvature). These functions are computed analytically and involve diffusive pseudo-differential operators, for which we have representation formula and input-output realizations, yielding direct numerical approximations of finite order. The method is based on some involved complex analysis.
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Thomas Hélie, Denis Matignon. Diffusive representations for the analysis and simulation of flared acoustic pipes with visco-thermal losses. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2006, vol. 16 (n° 4), pp. 503-536. ⟨10.1142/S0218202506001248⟩. ⟨hal-01373407⟩

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