Numerical modeling of a saxophone and comparison with experimental measurements

Saxophones making has long relied on craftsmanship, associated with an empirical knowledge of their acoustic functioning. The design process is now mainly based on the study of the input impedance, accessible experimentally or computationally. The numerical approaches are currently limited either by the accuracy (analytical models) or by the computation time (numerical resolution of PDEs). The challenge is to propose a numerical method combining both, to access the acoustic pressure and velocity fields in the instrument. Our objective was to develop a high-performance parallel numerical tool based on FEM to model accurately (a few cents on the resonances) the acoustic behavior of the resonator under playing conditions. The computation time was reduced by an order of magnitude compared to the brute force approach, using different modeling strategies specific to wind instruments: First, the modeling of the visco-thermal losses at the walls; then, the reduction of the size of the linear systems and finally, the reuse and model reduction to limit the effect of the multiple resolutions imposed by the wide frequency range of interest. The model is validated by comparison with experimental measurements. An impedance measurement system allowing acquisitions under controlled flow has been developed to reproduce realistic playing conditions.