  Taking advantage of an extended Lugiato--Lefever equation with third-order
dispersion, we numerically show that dark cavity solitons formed in normal
dispersion of microresonators are capable of emitting dispersive waves in both
normal and anomalous dispersion regions, resembling the behavior of the
commonly encountered bright cavity solitons. The generated dispersive waves can
be accurately predicted by the dissipative radiation theory. In addition, we
demonstrate the stability enhancement of Kerr frequency combs in normal
dispersion regime in case the dispersive wave is emitted by dark solitons in
presence of third-order dispersion.
