Passing waves from atomistic to continuum

Progress in the development of coupled atomistic–continuum methods for simulations of critical dynamic material behavior has been hampered by a spurious wave reflection problem at the atomistic–continuum interface. This problem is mainly caused by the difference in material descriptions between the atomistic and continuum models, which results in a mismatch in phonon dispersion relations. In this work, we introduce a new method based on atomistic dynamics of lattice coupled with a concurrent atomistic–continuum method to enable a full phonon representation in the continuum description. This permits the passage of short-wavelength, high-frequency phonon waves from the atomistic to continuum regions. The benchmark examples presented in this work demonstrate that the new scheme enables the passage of all allowable phonons through the atomistic–continuum interface; it also preserves the wave coherency and energy conservation after phonons transport across multiple atomistic–continuum interfaces. This work is the first step towards developing a concurrent atomistic–continuum simulation tool for non-equilibrium phonon-mediated thermal transport in materials with microstructural complexity.