Improved multimodal methods for the acoustic propagation in waveguides with finite wall impedance

We address the problem of acoustic propagation in waveguides with wall impedance, or Robin, boundary condition. Two improved multimodal methods are developed to remedy the problem of the low convergence of the series in the standard modal approach. In the first improved method, the series is enriched with an additional mode, which is thought to be able to restore the right boundary condition. The second improved method consists in a reformulation of the expansions able to restore the right boundary conditions for any truncation, similar to polynomial subtraction technique. Surprisingly, the first improved method is found to be the most efficient. Notably, the convergence of the scattering properties is increased from N ^-1 in the standard modal method to N ^-3 in the reformulation and N ^-5 in the formulation with a supplementary mode. The improved methods are shown to be of particular interest when surface waves are generated near the impedance wall.