  We present a procedure to determine transmission eigenchannels for coherent
phonon transport in nanoscale devices using the framework of nonequilibrium
Green's functions. We illustrate our procedure by analyzing a one-dimensional
chain, where all steps can be carried out analytically. More importantly, we
show how the procedure can be combined with ab initio calculations to provide a
better understanding of phonon heat transport in realistic atomic-scale
junctions. In particular, we study the phonon eigenchannels in a gold metallic
atomic-size contact and different single-molecule junctions based on molecules
such as an alkane chain, C$_{60}$, and a brominated benzene-diamine, where in
this latter case destructive phonon interference effects take place.
