Physical modeling of a conical lip reed instrument

A model of a brass instrument is described in which the air flow and pressure inside the instrument are computed with the Navier-Stokes equations and the motion of the player's lips are described using the swinging lip model of Adachi and Sato [J. Acoust. Soc. Am. 99, 1200-1209 (1996)]. Using the Navier-Stokes equations to treat the air motion allows the calculation of the spatial variations and time dependences of the pressure and velocity near the lips, which has not been possible with previous modeling approaches. Detailed results for these quantities and for the lip motion are presented, and compared with the results of previous modeling of lip reed instruments and with available experimental results. Shortcomings are found in previous treatments of the aerodynamic force on the lips, and the implications of this result for first-principles modeling of brass instruments are discussed.