Multiphysics wave simulator for generalized porous media across scales

Wave propagation in the de la Cruz and Spanos (dCS) multiphysics porous media theory accounts for an additional slow S wave, fundamental in the representation of fluid shear motion at high frequencies and absent from Biot (BT) theory. In this paper, a coupled hydro-mechanical finite element method is presented for a dCS porous media. The formulation is dynamic, and expressed in terms of solid displacement u s , fluid pressure p , and relative fluid velocity w . A verification study showed that the BT theory can be recovered as a particular case of the dCS model, and comparison with analytical solutions showed great agreement. The convergence study confirmed optimal rates for mesh refinement and time step size. Two-dimensional numerical examples highlight the multiscale aspect of the model through the simulation of low- and high-frequency regimes and large- and small-length scale cases. Variations in non-reciprocal solid–fluid interactions were more noticeable for the fluid and porosity fields. The results show that differences between BT and dCS models are more pronounced for laboratory-scale high-frequency problems. The developed fully coupled model is a robust tool for wave propagation simulation employing a generalized multiscale porous media theory. • Derivation of coupled hydro-mechanical formulation for dCS porous media theory • Optimal spatial convergence rates for first order polynomial approximation • Time integration scheme verified through step refinement and spectral analysis • Monolithic hydro-mechanical simplified dCS model yield same results as Biot theory • Laboratory-scale high-frequency simulation had discrepancies in Biot and dCS models • Simulations for multiple wavelength scales pictured reflected and transmitted waves.