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Despite their success in microscale modeling of materials, atomistic methods are still limited by short time scales, small domain sizes, and high strain rates. Multiscale formulations can capture the continuum-level response of solids over longer runtimes, but using such schemes to model highly dynamic, nonlinear phenomena is very challenging and an active area of research. In this work, we develop novel techniques within the concurrent atomistic-continuum multiscale framework to simulate shock wave propagation through a two-dimensional, single-crystal lattice. The technique is described in detail, and two moving window methods are incorporated to track the shock front through the domain and thus prevent spurious wave reflections at the atomistic-continuum interfaces. We compare our simulation results to analytical models as well as previous atomistic and CAC data and discuss the apparent effects of lattice orientation on the shock response of FCC crystals. We then use the moving window techniques to perform parametric studies which analyze the shock front's structure and planarity. Finally we compare the efficiency of our model to molecular dynamics simulations. This work showcases the power of using a moving window concurrent multiscale framework to simulate dynamic shock evolution over long runtimes and opens the door to more complex studies involving shock propagation through composites and high-entropy alloys.