Time domain numerical modeling of wave propagation in poroelastic media with Chebyshev rational approximation of the fractional attenuation
Date
2022-08-16
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematical Methods in the Applied Sciences
Abstract
In 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.
Description
This 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.
Keywords
Biot-JKD model, Chebyshev approximation, poroelastic media, RKDG method, splitting method, stiff system, temporal convolution
Citation
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