Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives
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.
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives. Journal of Computational Physics, Elsevier, 2013, 237, pp.1-20. ⟨10.1016/j.jcp.2012.12.003⟩. ⟨hal-00713127v2⟩
Journal: Journal of Computational Physics
Date de publication: 01-01-2013