  A kinetic model called the $\nu$-model is proposed to replace the complicated
Boltzmann collision operator in the simulation of rarefied flows of monatomic
gas. The model follows the relaxation-time approximation, but the collision
frequency (i.e, inverse relaxation time) is a function of the molecular
velocity to reflect part of the collision details of the Boltzmann equation,
and the target velocity distribution function (VDF) to which the VDF relaxes is
close to that used in the Shakhov model. Based on the numerical simulation of
strong non-equilibrium shock waves, a half-theoretical and half-empirical
collision frequency is designed for different intermolecular potentials: the
$\nu$-model shows significantly improved accuracy, and the underlying mechanism
is analysed. The $\nu$-model also performs well in canonical rarefied
micro-flows, especially in the thermal transpiration, where the conventional
kinetic models with velocity-independent collision frequency lack the
capability to distinguish the influence of intermolecular potentials.
