Time-domain Modeling of Elastic and Acoustic Wave Propagation in Unbounded Media with Application to Metamaterials

Perfectly matched layers (PML) are a well-developed method for simulating wave propagation in unbounded media enabling the use of a reduced computational domain without having to worry about spurious boundary reflections. Many PML studies have been reported for both acoustic waves in fluids and elastic waves in solids. Nevertheless, further studies are needed for improvements in the fields of formulation, stability, and inhomogeneity of PMLs. This thesis introduces new second-order time-domain PML formulations for modeling mechanical wave propagation in unbounded solid, fluid, and coupled fluid-solid media. It also addresses certain stability issues, and demonstrates application of these formulations. Using a complex coordinate stretching approach a PML for the time-domain anisotropic elastic wave equation in two dimensional space is compactly formulated with two second- order equations along with only four auxiliary equations. This makes it smaller than existing formulations, thereby simplifying the problem and reducing the computational burden. A simple method is proposed for improving the stability of the discrete PML problem for a wide range of otherwise unstable anisotropic elastic media. Specifically, the value of the scaling parameter was increased thereby moving unstable modes out of the discretely resolved range of spatial frequencies. A new second-order time-domain PML formulation for fluid-solid heterogeneous media is presented. This formulation satisfies the interface coupling boundary conditions which were chosen such that they can be readily integrated into a weak formulation of the complete fluid-solid problem and which can be used in a finite element method (FEM) analysis. Numerical FEM results are given to establish the accuracy of the formulations and to provide examples of their application. In particular, numerical examples are shown to validate the elastic wave PML formulation and to illustrate the improved stability that can be achieved with certain anisotropic media that have known issues. In addition, the effectiveness of the fluid-solid PML is numerically demonstrated for absorbing all kinds of bulk waves, as well as surface and evanescent waves. Finally, the new formulations were used to predict the transient response of a solid phononic structure consisting of a superfocusing acoustic lens.Ph.D