Acoustic Propagation in lined ducts with varying cross-section using a Mild-Slope approximation

TL;DR

This paper introduces a simplified 1D acoustic mild-slope equation for modeling low-frequency sound propagation in ducts with varying cross-sections and lining, offering a computationally efficient alternative to Helmholtz equation solutions.

Contribution

The paper derives a novel 1D acoustic mild-slope equation using the Galerkin method for ducts with smoothly varying lining and cross-section, providing a new modeling approach.

Findings

The acoustic mild-slope equation closely matches FEM Helmholtz solutions.

The method reduces computational cost compared to traditional Helmholtz-based models.

Good agreement observed in low-frequency sound propagation simulations.

Abstract

A modelling of low-frequency sound propagation in slowly varying ducts with smoothly varying lining is proposed leading to an acoustic mild-slope equation analogue to the with mild-slope equation for water waves. This simple 1D Mild Slope Equation is derived by direct application of the Galerkin method. It is shown that the acoustic mild-slope equation can serve as a good alternative to computationally expensive Helmholtz equations to solve such kind of problem. The results from this equation agrees well with FEM based solutions of Helmholtz equation.