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Energy analysis and discretization of the time-domain equivalent fluid model for wave propagation in rigid porous media

Moufid, Ilyes and Matignon, Denis and Roncen, Rémi and Piot, Estelle Energy analysis and discretization of the time-domain equivalent fluid model for wave propagation in rigid porous media. (2022) Journal of Computational Physics, 451. 110888. ISSN 0021-9991

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Official URL: https://doi.org/10.1016/j.jcp.2021.110888

Abstract

The equivalent fluid model (EFM) describes the acoustic properties of rigid porous media by defining the intra-pore fluid phase as a fluid with an effective density and an effective compressibility. Their definitions are based on the dynamic tortuosity α and the normalized dynamic compressibility β. These physical quantities are complex-valued functions depending on the frequency, and can be irrational as in the Johnson-Champoux-Allard-Pride-Lafarge (JCAPL) model. Hence, the system of equations derived from the EFM can involve fractional derivatives in the time domain. This paper presents an approach to formulate the EFM equations described by the JCAPL model in the time domain, leading to an augmented system for which a proof of stability is given. From the EFM, a model for numerical simulation is built with α and β approximated using a multipole model. Sufficient stability conditions are then provided for the multipole-based EFM. Lastly, a numerical analysis is carried out in order to illustrate the theoretical results and a simulation of the impedance tube experiment is presented.

Item Type:Article
HAL Id:hal-03515490
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE)
Laboratory name:
Funders:
EUR TSAE under grant ANR-17-EURE-0005
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Deposited On:06 Jan 2022 16:33

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