Improved multimodal formulation of the wave propagation in a 3D waveguide with varying cross-section and curvature

An efficient method is proposed to solve the multimodal wave propagation within a three-dimensional waveguide bounded by a hard wall with varying cross section and curvature. This is achieved by first turning the original problem, in a complex-shaped waveguide, into a cylindrical waveguide with unit radius, by means of an adapted and flexible geometrical transformation. Then supplementary modes are defined to enrich the standard modal basis that is usually considered in such methods and to help restore the right boundary condition. It is shown through various numerical applications that the introduction of these supplementary modes, whatever the complexity of the waveguide geometry, significantly enhances the multimodal method, notably by increasing its convergence rate, whether one's aim is to solve the wavefield or the scattering problem.