The scattering of scalar waves by a periodic row of inclusions is theoretically and numerically investigated. The wavelength in the background medium is assumed to be much larger than the typical sizes of the inclusions. The latter are also much softer than the matrix, yielding localized resonances within the microstructure. Previous works in the inviscid case have concerned: (i) the derivation of effective resonant jump conditions, that are non local in time (Touboul et al. (2020) [41]); (ii) the introduction of auxiliary fields along the interface, providing a time-domain formulation of the scattering problem (Touboul et al. (2020) [40]). The present contribution extends the analysis to dissipative cases, which allows to be closer from real devices. The effective jump conditions with damping are obtained, both in the frequency domain and in the time domain. An exact plane-wave solution is proposed. A balance of energy is written, and new auxiliary fields are introduced. Practical implementation of the simulation methods is discussed. Then, numerical experiments are proposed to validate the auxiliary-field approach. The effect of dissipation is examined, and the relevance of the homogenized simulations in comparison with full-field simulations of transient waves is assessed. As an application, a numerical experiment of Coherent Perfect Absorption is finally proposed: at critical values of the attenuation parameter and close to the resonant frequencies, the waves impacting the dissipative resonant interface are fully absorbed.

从理论上和数值上研究了周期性包裹体行对标量波的散射。假设背景介质中的波长远大于包裹体的典型尺寸。后者也比基体软得多，在微观结构内产生局部共振。以前在无粘性情况下的工作涉及：（i）有效共振跳跃条件的推导，在时间上是非局部的（Touboul 等人（2020）[41]）；(ii) 沿界面引入辅助场，提供散射问题的时域公式（Touboul et al. (2020) [40]）。目前的贡献将分析扩展到耗散情况，这允许更接近真实设备。获得具有阻尼的有效跳跃条件，在频域和时域中。提出了精确的平面波解决方案。写入了能量平衡，并引入了新的辅助场。讨论了模拟方法的实际实施。然后，提出了数值实验来验证辅助场方法。检查耗散的影响，并评估均质模拟与瞬态波全场模拟的相关性。作为应用，最终提出了相干完美吸收的数值实验：在衰减参数的临界值和接近谐振频率处，冲击耗散谐振界面的波被完全吸收。讨论了模拟方法的实际实施。然后，提出了数值实验来验证辅助场方法。检查耗散的影响，并评估均质模拟与瞬态波全场模拟的相关性。作为应用，最终提出了相干完美吸收的数值实验：在衰减参数的临界值和接近谐振频率处，冲击耗散谐振界面的波被完全吸收。讨论了模拟方法的实际实施。然后，提出了数值实验来验证辅助场方法。检查耗散的影响，并评估均质模拟与瞬态波全场模拟的相关性。作为应用，最终提出了相干完美吸收的数值实验：在衰减参数的临界值和接近谐振频率处，冲击耗散谐振界面的波被完全吸收。并且评估了与瞬态波的全场模拟相比的均质化模拟的相关性。作为应用，最终提出了相干完美吸收的数值实验：在衰减参数的临界值和接近谐振频率处，冲击耗散谐振界面的波被完全吸收。并且评估了与瞬态波的全场模拟相比的均质化模拟的相关性。作为应用，最终提出了相干完美吸收的数值实验：在衰减参数的临界值和接近谐振频率处，冲击耗散谐振界面的波被完全吸收。