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.