Acoustic wave propagation in inhomogeneous, layered waveguides based on modal expansions and hp-FEM

• Coupled-mode model for propagation/scattering in inhomogeneous, layered waveguides.
• Modal expansion enhanced by additional terms for sloping boundaries and interfaces.
• hp-FEM for local vertical eigenvalue problems and the horizontal coupled mode system.
• Simulations showing the role of additional modes and the convergence of the method.
• The method can be naturally extended to efficiently treat stratified 3D waveguides.

A new model is presented for harmonic wave propagation and scattering problems in non-uniform, stratified waveguides, governed by the Helmholtz equation. The method is based on a modal expansion, obtained by utilizing cross-section basis defined through the solution of vertical eigenvalue problems along the waveguide. The latter local basis is enhanced by including additional modes accounting for the effects of inhomogeneous boundaries and/or interfaces. The additional modes provide implicit summation of the slowly convergent part of the local-mode series, rendering the remaining part to be fast convergent, increasing the efficiency of the method, especially in long-range propagation applications. Using the enhanced representation, in conjunction with an energy-type variational principle, a coupled-mode system of equations is derived for the determination of the unknown modal-amplitude functions. In the case of multilayered environments, hh- and pp-FEM have been applied for the solution of both the local vertical eigenvalue problems and the resulting coupled mode system, exhibiting robustness and good rates of convergence. Numerical examples are presented in simple acoustic propagation problems, illustrating the role and significance of the additional mode(s) and the efficiency of the present model, that can be naturally extended to treat propagation and scattering problems in more complex 3D waveguides.