Numerical modeling of 1-D transient poroelastic waves in the low-frequency range
This work addresses the numerical challenge of modeling both fast and slow waves in porous media for geophysics or civil engineering applications, but it is incremental as it combines existing techniques.
The authors developed a numerical method combining ADER scheme, space-time mesh refinement, and interface conditions to model 1-D transient poroelastic waves in the low-frequency range, validated against analytical solutions.
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.