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

TL;DR

This paper presents a numerical method for simulating 1D transient poroelastic waves in porous media using Biot's model, combining advanced schemes to accurately capture both fast and slow wave phenomena.

Contribution

A novel numerical approach integrating ADER scheme, mesh refinement, and interface methods for efficient 1D poroelastic wave modeling.

Findings

Validated against analytical solutions.

Accurately captures coexistence of fast and slow waves.

Demonstrates effectiveness of combined numerical tools.

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.