Abstract A finite volume full-wave method is used to simulate nonlinear dissipative acoustic propagation in ducts with a circular cross-section. Thermoviscous dissipative effects, due to bulk viscosity and shear viscosity in the boundary layer adjacent to the duct walls, are also considered. The propagation is assumed to be axisymmetric, and two different geometries are considered: a straight cylindrical tube, and a cylindrical tube joined smoothly to a slowly-flaring bell. Of special interest is the study of the onset of standing waves in the nonlinear regime. The full-wave numerical scheme is particularly well-adapted for this purpose, as it is not necessary to impose boundary conditions at the open end of the duct. A simplified model of excitation is adopted, where the lips are replaced by a spring–mass system which behaves like a pressure valve with a single degree of freedom. The full system behaves as expected, with a feedback cycle established between the pressure valve and the air column. The simulation is validated successfully in the linear regime using a theoretical solution. It is shown that increasing the stiffness of the lips leads to discrete jumps in playing frequency, which is behaviour typical of brass instruments. In the nonlinear regime, shock formation is observed for sufficiently high amplitudes of oscillation, and the radiation of these shock waves by the open end of the ducts can be visualised in the time-domain, along with edge-diffraction effects. The formation and evolution of standing waves in the nonlinear regime, where the effect of these shocks is very noticeable, is also examined.

中文翻译：

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管乐器非线性耗散声驻波全波数值模拟

摘要 用有限体积全波法模拟圆形截面管道中的非线性耗散声传播。由于与管道壁相邻的边界层中的体积粘度和剪切粘度，热粘性耗散效应也被考虑在内。假设传播是轴对称的，并考虑两种不同的几何形状：直圆柱管和平滑连接到缓慢张开的钟形管的圆柱管。特别感兴趣的是研究非线性区域中驻波的开始。全波数值方案特别适用于此目的，因为不必在管道的开口端施加边界条件。采用简化的励磁模型，其中唇部被弹簧质量系统取代，该系统的行为类似于具有单一自由度的压力阀。整个系统按预期运行，在压力阀和气柱之间建立了一个反馈循环。使用理论解决方案在线性状态下成功验证了模拟。结果表明，增加嘴唇的刚度会导致演奏频率的离散跳跃，这是铜管乐器的典型行为。在非线性状态下，可以观察到足够高振幅的激波形成，并且可以在时域中可视化管道开口端的这些激波辐射以及边缘衍射效应。在非线性状态下驻波的形成和演化，这些冲击的影响非常明显，