The ghost solid method for the elastic solid-solid interface

In this work, three variants of Ghost Solid Method (GSM) are proposed for application to the boundary conditions at the solid-solid interface of isotropic linearly elastic materials, in a Lagrangian framework. It is shown that, in the presence of the wave propagation through the solid-solid mediums, the original GSM [1] can lead to non-physical oscillations in the solution, even for first-order solvers. It is discussed and numerically shown that these oscillations will be more severe if a higher order solver is employed using the original GSM. A scheme for prediction of these non-physical oscillations at the interface is also introduced. The other two variants of GSM proposed, however, can remove the non-physical oscillations that may rise at the interface. Next, the extension to two-dimensional settings with slip and no-slip conditions at the interface is carried out. Numerous numerical examples in one- and two-dimensional settings are provided attesting to the viability and effectiveness of the GSM for treating wave propagation at the solid-solid interface.