Numerical modeling of 1-D transient poroelastic waves in the low-frequency range

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

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

Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot's model with frequency-independant coefficients. The coexistence of a propagating fast wave and a diffusive slow wave makes numerical modeling tricky. A method combining three numerical tools is proposed: a fourth-order ADER scheme with time-splitting to deal with the time-marching, a space-time mesh refinement to account for the small-scale evolution of the slow wave, and an interface method to incorporate the jump conditions at interfaces. Comparisons with analytical solutions confirm the validity of this approach.

Mots clés: Elastic waves; Porous media; Biot's model; Time-splitting; ADER schemes; Space-time mesh refinement; Immersed interface method.; Immersed interface method

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]; Analyse numérique [math.NA]; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]

Guillaume Chiavassa, Bruno Lombard, Joël Piraux. Numerical modeling of 1-D transient poroelastic waves in the low-frequency range. 2007. ⟨hal-00193103v1⟩