Numerical Simulation of Acoustic Waveguides for Webster-Lokshin Model Using Diffusive Representations

This paper deals with the numerical simulation of acoustic wave propagation in axisymmetric waveguides with varying cross-section using a Webster-Lokshin model. Splitting the pipe into pieces on which the model coefficients are nearly constant, analytical solutions are derived in the Laplace domain, enabling for the realization of the propagation by concatenating scattering matrices of transfer functions (§2). These functions involve standard differential and delay operators, as well as pseudo-differential operators of diffusive type, induced by both the viscothermal losses and the curvature. These operators are explicitly decomposed thanks to an asymptotic expansion, and the diffusive ones may be defined and classified (§3). Various equivalent diffusive realizations may be proposed, that are deeply linked to choices of cuts in the complex analysis of the transfer functions. Then, finite order approximations are given for their simulation (§4).