  Thermal wall is a convenient idealization of a rapidly vibrating plate used
for vibrofluidization of granular materials. The objective of this work is to
incorporate the Knudsen temperature jump at thermal wall in the Navier-Stokes
hydrodynamic modeling of dilute granular gases of monodisperse particles that
collide nearly elastically. The Knudsen temperature jump manifests itself as an
additional term, proportional to the temperature gradient, in the boundary
condition for the temperature. Up to a numerical pre-factor of order unity,
this term is known from kinetic theory of elastic gases. We determine the
previously unknown numerical pre-factor by measuring, in a series of molecular
dynamics (MD) simulations, steady-state temperature profiles of a gas of
elastically colliding hard disks, confined between two thermal walls kept at
different temperatures, and comparing the results with the predictions of a
hydrodynamic calculation employing the modified boundary condition. The
modified boundary condition is then applied, without any adjustable parameters,
to a hydrodynamic calculation of the temperature profile of a gas of inelastic
hard disks driven by a thermal wall. We find the hydrodynamic prediction to be
in very good agreement with MD simulations of the same system. The results of
this work pave the way to a more accurate hydrodynamic modeling of driven
granular gases.
