Shock transmission and reflection from a material interface and subsequent reflection from a hard boundary

As a shock wave passes through a material interface into a region of higher density (the receiver material), a trans- mitted and reflected shock wave are both generated and the interface is set into motion. The speeds of the transmitted shock, reflected shock, and interface are related to the ini- tial shock speed and material properties via a set of coupled nonlinear equations that, in general, cannot be easily solved analytically. In this report, we derive the equations which describe this process and we document a numerical routine which solves the nonlinear equations. We then go on to solve the problem of finding the position where the interface col- lides with the transmitted shock wave once the transmitted shock wave is reflected from an impenetrable boundary lo- cated somewhere away from the initial material interface. Fi- nally, we compare the analytical predictions with the CALE simulation running in 1-D