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Numerical modeling of 1D transient poroelastic waves in the low-frequency range. (English) Zbl 1407.74043

Summary: Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot model with frequency-independent 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.

MSC:

74J05 Linear waves in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

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References:

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