A perfectly matched layer formulation for modeling transient wave propagation in an unbounded fluid-solid medium

Wave propagation in an infinite medium can be numerically simulated by surrounding a finite region by a perfectly matched layer (PML). When the medium is heterogeneous consisting of both solids and liquids, careful consideration is needed in specifying the properties of the PML especially because parts of it lie at the solid-fluid interface. While such a situation could arise in many important fields including marine seismology, where water is in contact with earth, and in biomedical ultrasound, where soft tissue is in contact with bone, no PML formulation exists to appropriately model such coupled problems. Here, a second-order time-domain PML formulation for fluid-solid heterogeneous media in two dimensions that satisfies the interface coupling boundary condition throughout the computational domain is presented. Numerical results are given to establish the applicability and accuracy of such a PML formulation in discrete settings without causing stability issues, spurious reflections, or any other problems. In particular, the effectiveness of the PML in absorbing all kinds of bulk waves, as well as surface and evanescent waves, is studied.