Time domain numerical modeling of wave propagation in poroelastic media with Chebyshev rational approximation of the fractional attenuation

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Author(s)Xie, Jiangming
Author(s)Li, Maojun
Author(s)Ou, Miao-Jung Yvonne
Date Accessioned2022-09-13T19:21:07Z
Date Available2022-09-13T19:21:07Z
Publication Date2022-08-16
DescriptionThis is the peer reviewed version of the following article: Xie, J, Li, M, Ou, M-JY. Time domain numerical modeling of wave propagation in poroelastic media with Chebyshev rational approximation of the fractional attenuation. Math Meth Appl Sci. 2022; 1- 23. doi:10.1002/mma.8630, which has been published in final form at https://doi.org/10.1002/mma.8630. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. This article will be embargoed until 8/16/2023.en_US
AbstractIn this work, we investigate the poroelastic waves by solving the time-domain Biot-JKD equation with an efficient numerical method. The viscous dissipation occurring in the pores depends on the square root of the frequency and is described by the Johnson-Koplik-Dashen (JKD) dynamic tortuosity/permeability model. The temporal convolutions of order 1/2 shifted fractional derivatives are involved in the time-domain Biot-JKD model, causing the problem to be stiff and challenging to be implemented numerically. Based on the best relative Chebyshev approximation of the square-root function, we design an efficient algorithm to approximate and localize the convolution kernel by introducing a finite number of auxiliary variables that satisfy a local system of ordinary differential equations. The imperfect hydraulic contact condition is used to describe the interface boundary conditions and the Runge-Kutta discontinuous Galerkin (RKDG) method together with the splitting method is applied to compute the numerical solutions. Several numerical examples are presented to show the accuracy and efficiency of our approach.en_US
SponsorThe work of J. Xie is partially supported by NSFC Grants (nos. 12171274 and 12171465). The work of M. Li is partially supported by a NSFC Grant (no. 11871139). MYO's work was partial sponsored by US NSF Grants DMS-1413039 and DMS-1821857.en_US
CitationXie, J, Li, M, Ou, M-JY. Time domain numerical modeling of wave propagation in poroelastic media with Chebyshev rational approximation of the fractional attenuation. Math Meth Appl Sci. 2022; 1- 23. doi:10.1002/mma.8630en_US
ISSN1099-1476
URLhttps://udspace.udel.edu/handle/19716/31351
Languageen_USen_US
PublisherMathematical Methods in the Applied Sciencesen_US
KeywordsBiot-JKD modelen_US
KeywordsChebyshev approximationen_US
Keywordsporoelastic mediaen_US
KeywordsRKDG methoden_US
Keywordssplitting methoden_US
Keywordsstiff systemen_US
Keywordstemporal convolutionen_US
TitleTime domain numerical modeling of wave propagation in poroelastic media with Chebyshev rational approximation of the fractional attenuationen_US
TypeArticleen_US
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