A model of a single reed instrument is studied in which the reed is described as an Euler-Bernoulli beam, and the air flow through the instrument is calculated using the Navier-Stokes equations. The hypothetical instrument resembles a clarinet, but is smaller than a real clarinet to keep the numerical modeling feasible on available supercomputers. This article explores the conditions under which the frequency of the reed oscillations and the emitted sound are determined by the resonant frequency of the bore of the instrument. The effect of the contact between the reed and the player's lips is also studied, and quantitative results for the air density and pressure in the mouthpiece and throughout the instrument bore are also presented.

中文翻译：

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基于Navier-Stokes的单簧管模型

研究了单个芦苇乐器的模型，其中将芦苇描述为欧拉-伯努利射束，并使用Navier-Stokes方程计算通过该乐器的空气流量。假设的仪器类似于单簧管，但小于实际的单簧管，以使数值模型在可用的超级计算机上可行。本文探讨了在哪些条件下簧片振荡的频率和发出的声音取决于乐器孔的共振频率。还研究了簧片和演奏者嘴唇之间接触的影响，并给出了吹嘴和整个乐器孔中空气密度和压力的定量结果。