  This article develops the design of a sound synthesis model of a woodwind
instrument by modal decomposition of the input impedance, taking into account
viscothermal losses as well as localized nonlinear losses at the end of the
resonator. This formalism has already been applied by Diab et al. (2022) to the
study of forced systems. It is now implemented for self-oscillating systems.
The employed method extends the denition of the input impedance to the
nonlinear domain by adding a dependance on the RMS acoustic velocity at a
geometric discontinuity. The poles and residuals resulting from the modal
decomposition are interpolated as a function of this velocity. Thus, the
pressure-ow relation dened by the resonator is completed by new equations which
account for the dependence with the velocity at the end of the tube. To assess
the ability of the model to reproduce a real phenomenon, comparisons with the
experimental results of Atig et al. (2004) and Dalmont et al. (2007) were
carried out. Simulations show that the model reproduces these experimental
results qualitatively and quantitatively.
