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Time-domain numerical modeling of wave propagation in poroelastic media with rational approximation of the fractional attenuation
  • Jiangming Xie,
  • Maojun Li,
  • Miao-Jung Ou
Jiangming Xie
Tsinghua University

Corresponding Author:xiejiangming@mail.tsinghua.edu.cn

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Maojun Li
University of Electronic Science and Technology of China
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Miao-Jung Ou
University of Delaware
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n 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 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.
09 Dec 2021Submitted to Mathematical Methods in the Applied Sciences
11 Dec 2021Submission Checks Completed
11 Dec 2021Assigned to Editor
17 Dec 2021Reviewer(s) Assigned
13 Apr 2022Review(s) Completed, Editorial Evaluation Pending
13 Apr 2022Editorial Decision: Revise Major
21 Apr 20221st Revision Received
22 Apr 2022Submission Checks Completed
22 Apr 2022Assigned to Editor
11 May 2022Reviewer(s) Assigned
19 Jul 2022Review(s) Completed, Editorial Evaluation Pending
21 Jul 2022Editorial Decision: Accept