Atomistic methods have successfully modeled different aspects of shock wave propagation in materials over the past several decades, but they suffer from limitations which restrict the total runtime and system size. Multiscale methods have been able to increase the length and time scales that can be modeled but employing such schemes to simulate wave propagation and evolution through engineering-scale domains is an active area of research. In this work, we develop two distinct moving window approaches within a Concurrent Atomistic–Continuum (CAC) framework to model shock wave propagation through a one-dimensional monatomic chain. In the first method, the entire CAC system travels with the shock in a conveyor fashion and maintains the shock front in the middle of the overall domain. In the second method, the atomistic region follows the shock by the simultaneous coarsening and refinement of the continuum regions. The CAC and moving window frameworks are verified through dispersion relation studies and phonon wave packet tests. We achieve good agreement between the simulated shock velocities and the values obtained from theory with the conveyor technique, while the coarsen-refine technique allows us to follow the propagating wave front through a large-scale domain. This work showcases the ability of the CAC method to accurately simulate propagating shocks and also demonstrates how a moving window technique can be used in a multiscale framework to study highly nonlinear, transient phenomena.

在过去的几十年里，原子方法已经成功地模拟了材料中冲击波传播的不同方面，但它们受到限制总运行时间和系统大小的限制。多尺度方法已经能够增加可建模的长度和时间尺度，但采用此类方案通过工程尺度域模拟波的传播和演化是一个活跃的研究领域。在这项工作中，我们在并发原子连续体 (CAC) 框架内开发了两种不同的移动窗口方法，以模拟冲击波通过一维单原子链的传播。在第一种方法中，整个 CAC 系统以传送带的方式与激波一起行进，并将激波前沿保持在整个域的中间。在第二种方法中，原子区通过连续区的同时粗化和细化来跟随冲击。CAC 和移动窗口框架通过验证色散关系研究和声子波包测试。我们在模拟的冲击速度和从理论获得的值之间取得了很好的一致性，使用传送带技术，而粗化-细化技术允许我们通过大尺度域跟踪传播波前。这项工作展示了 CAC 方法准确模拟传播冲击的能力，并展示了如何在多尺度框架中使用移动窗口技术来研究高度非线性的瞬态现象。