  The shear viscosity in the dilute regime of a model for confined granular
matter is studied by simulations and kinetic theory. The model consists on
projecting into two dimensions the motion of vibrofluidized granular matter in
shallow boxes by modifying the collision rule: besides the restitution
coefficient that accounts for the energy dissipation, there is a separation
velocity that is added in each collision in the normal direction. The two
mechanisms balance on average, producing stationary homogeneous states.
Molecular dynamics simulations show that in the steady state the distribution
function departs from a Maxwellian, with cumulants that remain small in the
whole range of inelasticities. The shear viscosity normalized with stationary
temperature presents a clear dependence with the inelasticity, taking smaller
values compared to the elastic case. A Boltzmann-like equation is built and
analyzed using linear response theory. It is found that the predictions show an
excellent agreement with the simulations when the correct stationary
distribution is used but a Maxwellian approximation fails in predicting the
inelasticity dependence of the viscosity. These results confirm that transport
coefficients depend strongly on the mechanisms that drive them to stationary
states.
