These authors use periodic boundary conditions in the directions;
the upper and lower boundaries are replaced by layers containing trapped
particles. The upper layer has a mean velocity while the bottom
layer is at rest.
Moving boundary region: the wall particles remain trapped in
the layer. An external force keeps up the relative velocity of the
upper and lower boundary layers.
The desired shear rate is
. We need an external
to achieve this. This force is proportional to the viscosity.
Again, the temperature will slowly increase due to the work done
by the external force.
F. J. Vesely / University of Vienna