  A time-domain numerical modeling of brass instruments is proposed. On one
hand, outgoing and incoming waves in the resonator are described by the
Menguy-Gilbert model, which incorporates three key issues: nonlinear wave
propagation, viscothermal losses, and a variable section. The non-linear
propagation is simulated by a TVD scheme well-suited to non-smooth waves. The
fractional derivatives induced by the viscothermal losses are replaced by a set
of local-in-time memory variables. A splitting strategy is followed to couple
optimally these dedicated methods. On the other hand, the exciter is described
by a one-mass model for the lips. The Newmark method is used to integrate the
nonlinear ordinary differential equation so-obtained. At each time step, a
coupling is performed between the pressure in the tube and the displacement of
the lips. Finally, an extensive set of validation tests is successfully
completed. In particular, self-sustained oscillations of the lips are simulated
by taking into account the nonlinear wave propagation in the tube. Simulations
clearly indicate that the nonlinear wave propagation has a major influence on
the timbre of the sound, as expected. Moreover, simulations also highlight an
influence on playing frequencies, time envelopes and on the playability of the
low frequencies in the case of a variable lips tension.
