论文标题
对持久粘膜热声学的有效时间域边界条件的调查
Investigations of an effective time-domain boundary condition for quiscent viscothermal acoustics
论文作者
论文摘要
狭窄几何形状中声音传播的准确模拟需要考虑粘性和热损失。在这方面，最近在频率域声学中模拟粘质损失的有效边界条件最近在受欢迎程度上获得了普及。在这里，我们研究了这样一个边界条件的时间域类似物。我们发现边界条件的热部分在时域是被动的，而粘性部分则不是。更确切地说，我们证明了粘性部分负责呈指数增长的正常模式，其时间生长速率无限，这表明所考虑的模型不适合。开发了有限差异时间域方案，以模拟导管中有损耗的声音传播。如果忽略了粘性损失，则发现获得的传输特性与频域模拟非常吻合。在一般情况下，模拟经历了与理论发现非常一致的不稳定性。
Accurate simulations of sound propagation in narrow geometries need to account for viscous and thermal losses. In this respect, effective boundary conditions that model viscothermal losses in frequency-domain acoustics have recently gained in popularity. Here, we investigate the time-domain analogue of one such boundary condition. We find that the thermal part of the boundary condition is passive in time domain as expected, while the viscous part is not. More precisely, we demonstrate that the viscous part is responsible for exponentially growing normal modes with unbounded temporal growth rates, which indicates ill-posedness of the considered model. A finite-difference-time-domain scheme is developed for simulations of lossy sound propagation in a duct. If viscous losses are neglected the obtained transmission characteristics are found to be in excellent agreement with frequency-domain simulations. In the general case, the simulations experience an instability much in line with the theoretical findings.
