Abstract This work presents benchmark examples related to the modelling of sound absorbing porous media with rigid frame based on the periodic geometry of their microstructures. To this end, rigorous mathematical derivations are recalled to provide all necessary equations, useful relations, and formulae for the so-called direct multi-scale computations, as well as for the hybrid multi-scale calculations based on the numerically determined transport parameters of porous materials. The results of such direct and hybrid multi-scale calculations are not only cross verified, but also confirmed by direct numerical simulations based on the linearised Navier-Stokes-Fourier equations. In addition, relevant theoretical and numerical issues are discussed, and some practical hints are given.

中文翻译：

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基于微结构的吸声刚性框架多孔介质建模基准

摘要 这项工作提出了与基于其微观结构的周期性几何形状的刚性框架吸声多孔介质建模相关的基准示例。为此，回顾严格的数学推导，为所谓的直接多尺度计算以及基于数值确定的多孔输运参数的混合多尺度计算提供所有必要的方程、有用的关系和公式。材料。这种直接和混合多尺度计算的结果不仅得到了交叉验证，而且还得到了基于线性化纳维-斯托克斯-傅立叶方程的直接数值模拟的证实。此外，还讨论了相关的理论和数值问题，并给出了一些实用的提示。