Biot-JKD model: Simulation of 1D transient poroelastic waves with fractional derivatives

JOURNAL OF COMPUTATIONAL PHYSICS

卷:237

Article

Blanc, Emilie¹  Chiavassa, Guillaume²  Lombard, Bruno¹ 

[1] CNRS, UPR 7051, Lab Mecan & Acoust, F-13402 Marseille, France

[2] CNRS, UMR 7340, Cent Marseille & M2P2, F-13451 Marseille, France

关键词: Porous media;    Elastic waves;    Biot-JKD model;    Fractional derivatives;    Time splitting;    Finite difference methods;    Cartesian grid;   

DOI  :  10.1016/j.jcp.2012.12.003

来源: Elsevier

【 摘 要 】

A time-domain numerical modeling of Biot poroelastic waves is presented. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce order 1/2 shifted fractional derivatives involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Thanks to the dispersion relation, the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest. A splitting strategy is then applied numerically: the propagative part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solutions show the efficiency and the accuracy of this approach. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free