A Boundary Integral Formulation of an Acoustic Boundary Layer Model in 2D

TL;DR

This paper develops a boundary integral method for solving the 2D Helmholtz equation with visco-thermal boundary conditions, enabling accurate simulation of boundary layer effects in acoustic devices.

Contribution

It introduces a novel boundary integral formulation that efficiently handles visco-thermal boundary conditions using Fredholm second-kind integral equations.

Findings

Enables fast and accurate acoustic boundary layer simulations.

Provides a stable integral equation formulation for visco-thermal effects.

Improves modeling of narrow-feature acoustic devices.

Abstract

We present a boundary integral formulation of the Helmholtz equation with visco-thermal boundary conditions, in two dimensions. Such boundary conditions allow for the accurate simulation of viscous and thermal losses in the vicinity of the boundary, which are particularly relevant in acoustic devices with narrow features. Using cancellations between hyper-singular operators, a variant of the method of images technique, and analytic pre-conditioners, we derive integral equations that are Fredholm second-kind, up to the application of a boundedly invertible operator. This approach allows for the fast and accurate solution of acoustics problems with boundary layers.