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

Abstract : 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 enforce the jump conditions at interfaces. Comparisons with analytical solutions confirm the validity of this approach.
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Guillaume Chiavassa, Bruno Lombard, Joël Piraux. Numerical modeling of 1-D transient poroelastic waves in the low-frequency range. Journal of Computational and Applied Mathematics, Elsevier, 2010, 234, pp.1757-1765. 〈10.1016/j.cam.2009.08.025〉. 〈hal-00193103v2〉

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