Mathematical model for coupling a quasi-unidimensional perfect flow

TL;DR

This paper develops a coupled mathematical model combining Euler equations for perfect fluid flow with a linear boundary layer model, validated through numerical methods and applied to nonlinear wave phenomena in trombones.

Contribution

It introduces a novel coupled model integrating perfect flow and boundary layer effects for wind instrument acoustics, validated by numerical simulations.

Findings

Validated numerical software against analytical solutions.

Demonstrated application to nonlinear waves in trombones.

Provided a new framework for simulating wind instrument acoustics.

Abstract

Nonlinear acoustics of wind instruments conducts to study unidimensional fluid flows. From physically relevant approximations that are modelized with the thin layer Navier Stokes equations, we propose a coupled model where perfect fluid flow is described by the Euler equations of gas dynamics and viscous and thermal boundary layer is modelized by a linear equation. We describe numerical discretization, validate the associated software by comparison with analytical solutions and consider musical application of strongly nonlinear waves in the trombone.