One-dimensional moving window atomistic framework to model long-time shock wave propagation.

We develop a long-time moving window framework using Molecular Dynamics (MD) to model shock wave propagation through a one-dimensional chain of atoms. The domain is divided into a purely atomistic "window" region containing the shock wave flanked by boundary or "continuum" regions on either end. The dynamics of the window atoms are governed by classic MD equations of motion while continuum shock conditions are applied to the continuum atoms. Spurious wave reflections are removed by employing a damping band method using the Langevin thermostat applied locally to the continuum region. The moving window effect is achieved by adding/removing atoms to/from the window and boundary regions, and thus the shock wave front is focused at the center of the window region indefinitely. As a result, the required domain size is very small allowing us to model shock wave propagation for a long time. We simulate the shock through a one-dimensional chain of copper atoms using either the Lennard-Jones, modified Morse, or Embedded Atom Model (EAM) interatomic potential. We first perform verification studies to ensure proper implementation of the thermostat, potential functions, and damping band method, respectively. Next, we track the propagating shock and compare the actual shock velocity and average particle velocity to their corresponding analytical input values. From these comparisons, we optimize the linear shock Hugoniot relation for the given "lattice" orientation and compare these results to those in literature. When incorporated into the linear shock equation, these new Hugoniot parameters are shown to produce a stationary shock wave front. Finally, we perform one-dimensional moving window simulations of an unsteady, structured shock up to a few nanoseconds and characterize the increase in the shock front's width.