  The behavior of a supercooled polymer melt composed of short chains with ten
beads near an oscillating plate are simulated by using a hybrid simulation of
molecular dynamics (MD) and computational fluid dynamics (CFD). In the method,
the macroscopic dynamics are solved by using CFD, but, instead of using any
constitutive equations, a local stress is calculated by using a non-equilibrium
MD simulation associated at each lattice node in the CFD calculation. It is
seen that the local rheology of the melt varies considerably in a thin viscous
diffusion layer that arises near an oscillating plate. It is also found that
the local rheology of the melt is divided into the three different regimes,
i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes,
according to the local Deborah number $De$, which is defined with the Rouse or
$\alpha$ relaxation time, $\tau_R$ or $\tau_\alpha$, and the angular frequency
of the plate $\omega$ as $De^R$=$\omega\tau_R$ or
$De^\alpha$=$\omega\tau_\alpha$. The melt behaves as a viscous fluid when
$De^R\lesssim 1$, and the crossover between the liquid-like and solid-like
regime takes place around $De^\alpha\simeq 1$.
