Numerical resolution of a physical model of flute-like instruments: comparison between different approaches

Abstract

International audienceThe study of flute-like instruments involves several subfields of investigation such as acoustics of the waves in the pipe, hydrodynamics of a jet perturbed by an acoustic field and aeroacoustics of a jet/labium interaction. Historically, several models of flute-like instruments have been proposed, including the results from separated studies of the parts mentioned above. In this paper, such a model is written, taking into account the following elements: (1) hydrodynamics of a jet perturbed by an acoustic field, through a delay equation, corresponding to the convection of a perturbation of the jet from the flue exit to the labium, (2) aeroacoustics of a jet/labium interaction, through a nonlinear equation, which highlights the presence of a dipolar pressure source, (3)acoustics of the waves in the pipe, through a modal formulation, (4) nonlinear losses at the labium, through an additional nonlinear term. This description includes two non-linear terms, which require numerical solving. This paper aims at comparing different approaches in terms of the resolution of the non linear equations. The following aspects of the model behaviour are addressed: amplitude/frequency evolution along periodic branches, regime changes, hysteresis..