Perfectly matched layers for transient multiphase flow in deformable porous media

Perfectly matched layers (PMLs) are widely used as non-reflecting boundary treatments for truncated computational domains in transient wave simulations. In fully coupled poromechanics, where deformation interacts with pore-fluid pressures, spurious boundary reflections can contaminate both displacement fields and coupled pressure variables, obscuring physical interpretations and degrading solver robustness. The finite-element formulation uses skeleton displacement, pore-water pressure, and capillary pressure, together with a consistent complex-frequency-shifted convolutional PML (CPML) treatment introduced at the weak-form level. The CPML is implemented as a coefficient field over an exterior subdomain, with auxiliary memory variables updated locally at Gauss points; this allows standard element assembly while modifying the gradient operators (and associated coupling blocks) in the absorbing zone. Discrete equations are integrated in time using a Newmark update. Numerical examples compare CPML, truncated-domain, and extended-domain computations for both homogeneous and layered plane-strain benchmarks. The results show that CPML strongly suppresses late-time reflection content in displacements, pore-water pressure, and suction histories while reproducing the extended-domain response at substantially lower computational cost, and that this behavior persists in a heterogeneous two-layer medium with internal reflection and transmission at a material interface.