A 2D Time domain numerical method for the low frequency biot model

Guillaume Chiavassa (1, 2) , Bruno Lombard (3) , Joël Piraux (3)

1 M2P2 - Modélisation et Simulation Numérique (en mécanique des fluides)
2 ECM - École Centrale de Marseille
3 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

A numerical method is proposed to simulate the propagation of transient poroelastic waves across 2D heterogeneous media, in the low frequency range. A velocity-stress formulation of Biot's equations is followed, leading to a first-order system of partial differential equations. This system is splitted in two parts: a propagative one discretized by a fourth-order ADER scheme, and a diffusive one that is solved analytically. Near material interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. Lastly, an immersed interface method is implemented to accurately model the jump conditions between the different media and the geometry of the interfaces. Numerical experiments and comparisons with exact solutions confirm the efficiency and the accuracy of the approach.

Domaines: Modélisation et simulation; Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Guillaume Chiavassa, Bruno Lombard, Joël Piraux. A 2D Time domain numerical method for the low frequency biot model. 10eme Congrès Français d'Acoustique, Apr 2010, Lyon, France. CD-ROM (6 p.). ⟨hal-00460254⟩