The acoustic analog of the quantum black hole for airborne sound in two dimensions was denominated as an omnidirectional acoustic absorber by Climente et al. [see Appl. Phys. Lett., 100, 144103 (2012)], who characterized its absorbing properties without providing any theoretical support. The viscothermal losses of the underlying structure, which consists of an absorbing core and a surrounding gradient-index (GRIN) lens both made of periodic distributions of cylindrical rods, are here comprehensively studied by using the boundary element method (BEM) in two dimensions. It is shown that the numerical simulations in two dimensions reproduce fairly well the increase in absorption of the core when the GRIN lens is added and reveal that the discrepancy between measured and calculated values of absorbance is an artifact of the experimental setup. The possibility of independent calculation of viscous and thermal losses contributions in the two-dimensional (2D) BEM algorithm is employed for the comparison with a homogenization theory in which the cluster of cylinders is represented by a single fluidlike viscous cylinder with effective parameters. We conclude that viscous losses represent about 90% of the total energy dissipated in the core. The homogenization approach results are only 2% below the results calculated with 2D BEM, indicating that the effective parameters obtained by the homogenization are very accurate.

中文翻译：

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二维声学黑洞中的粘热效应：边界元方法

Climente等人将二维空气传播声的量子黑洞声学模拟命名为全向吸声器。[见申请。物理。利特，100, 144103 (2012)]，在没有提供任何理论支持的情况下描述了其吸收特性。底层结构的粘热损失由吸收芯和周围梯度指数 (GRIN) 透镜组成，两者均由圆柱棒的周期性分布构成，这里通过使用二维边界元法 (BEM) 进行全面研究。结果表明，当添加 GRIN 透镜时，二维数值模拟相当好地再现了纤芯吸收的增加，并揭示了测量值和计算值之间的吸光度值之间的差异是实验设置的人工产物。在二维 (2D) BEM 算法中独立计算粘性和热损失贡献的可能性用于与均质化理论进行比较，其中圆柱体由具有有效参数的单个流体状粘性圆柱体表示。我们得出的结论是，粘性损耗约占核心耗散总能量的 90%。均质化方法的结果仅比 2D BEM 计算的结果低 2%，表明均质化获得的有效参数非常准确。