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Thermal wall is a convenient idealization of a rapidly vibrating plate usedfor vibrofluidization of granular materials. The objective of this work is toincorporate the Knudsen temperature jump at thermal wall in the Navier-Stokeshydrodynamic modeling of dilute granular gases of monodisperse particles thatcollide nearly elastically. The Knudsen temperature jump manifests itself as anadditional term, proportional to the temperature gradient, in the boundarycondition for the temperature. Up to a numerical pre-factor of order unity,this term is known from kinetic theory of elastic gases. We determine thepreviously unknown numerical pre-factor by measuring, in a series of moleculardynamics (MD) simulations, steady-state temperature profiles of a gas ofelastically colliding hard disks, confined between two thermal walls kept atdifferent temperatures, and comparing the results with the predictions of ahydrodynamic calculation employing the modified boundary condition. Themodified boundary condition is then applied, without any adjustable parameters,to a hydrodynamic calculation of the temperature profile of a gas of inelastichard disks driven by a thermal wall. We find the hydrodynamic prediction to bein very good agreement with MD simulations of the same system. The results ofthis work pave the way to a more accurate hydrodynamic modeling of drivengranular gases.

The Knudsen temperature jump and the Navier-Stokes hydrodynamics of granular gases driven by thermal walls