A posteriori error estimates for Webster's equation in wave propagation

TL;DR

This paper develops an a posteriori error estimation method for the generalized Webster's equation, which models wave propagation in curved tubes, providing rigorous bounds on approximation errors derived from the wave equation.

Contribution

It introduces an a posteriori error estimation technique for the generalized Webster's equation, enhancing the understanding of approximation accuracy in wave propagation models.

Findings

Provides rigorous error bounds for Webster's equation approximations

Validates the a posteriori estimation method through theoretical analysis

Improves reliability of wave propagation simulations in curved structures

Abstract

We consider a generalised Webster's equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster's equation in generalised form has been rigorously derived in a previous article starting from the wave equation, and it approximates cross-sectional averages of the propagating wave. Here, the approximation error is estimated by an a posteriori technique.