  The Boltzmann collision operator for a dilute granular gas of inelastic rough
hard spheres is much more intricate than its counterpart for inelastic smooth
spheres. Now the one-body distribution function depends not only on the
translational velocity of the center of mass but also on the angular velocity
of the particle. Moreover, the collision rules couple both velocities,
involving not only the coefficient of normal restitution but also the
coefficient of tangential restitution. The aim of this paper is to propose an
extension to inelastic rough particles of a Bhatnagar-Gross-Krook-like kinetic
model previously proposed for inelastic smooth particles. The Boltzmann
collision operator is replaced by the sum of three terms representing: (i) the
relaxation to a two-temperature local equilibrium distribution, (ii) the action
of a nonconservative drag force proportional to the peculiar velocity, and
(iii) the action of a nonconservative torque equal to a linear combination of
the angular velocity and its mean value. The three coefficients in the force
and torque are fixed to reproduce the Boltzmann collisional rates of change of
the mean angular velocity and of the two granular temperatures (translational
and rotational). A simpler version of the model is also constructed in the form
of two coupled kinetic equations for the translational and rotational velocity
distributions. The kinetic model is applied to the simple shear flow steady
state and the combined influence of the two coefficients of restitution on the
shear and normal stresses and on the translational velocity distribution
function is analyzed.
