  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 then 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.
