Modelling of Poro-Acoustic Media

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-10-10 DOI:10.1007/s00245-025-10338-3

Isabelle Gruais

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Abstract

This paper deals with the homogenization of a binary three-dimensional structure made of damped Helmholtz resonators embedded in a rigid porous matrix when both parts of each resonator, namely the duct and the chamber, are filled with the same Stokes fluid and when the Darcy and Stokes flows are coupled by a Beavers–Joseph type condition. As the small period of the distribution shrinks to zero, we study the asymptotic behaviour of the flow when the permeability and transfer coefficients on the interface are of unity order in contrast with the periodic distribution of resonators characterized by highly conductive parallel thin ducts. To that aim the energetic procedure of homogenization is associated to the control-zone method taking into account the geometry of the microstructure and heterogeneities of the conductivity coefficients. The main result lies in the asymptotic behaviour of the periodic distribution in the binary medium characterized by a significant increase of conductivity in thin ducts whose everlasting action contrasts with their local vanishing volume. The dependence with respect to the relative thickness of the ducts is studied.

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多孔声介质的建模

本文研究了由嵌入刚性多孔矩阵的阻尼亥姆霍兹谐振器组成的二元三维结构的均匀化问题，当每个谐振器的两个部分（即管道和腔室）都充满相同的斯托克斯流体，并且当达西流和斯托克斯流由海狸-约瑟夫型条件耦合时。当分布的小周期缩小到零时，我们研究了界面上的渗透率和传递系数为一阶时流动的渐近行为，并与以高导电性平行薄导管为特征的谐振腔的周期分布进行了对比。为此，考虑到微观结构的几何形状和电导率系数的非均质性，均质化的能量过程与控制区方法相关联。主要结果在于二元介质中周期分布的渐近行为，其特征是薄导管中电导率的显著增加，其持久作用与其局部消失体积形成对比。研究了其与管道相对厚度的关系。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.