  Models and methods that are able to accurately and efficiently predict the
flows of low-speed rarefied gases are in high demand, due to the increasing
ability to manufacture devices at micro and nano scales. One such model and
method is a Fokker-Planck approximation to the Boltzmann equation, which can be
solved numerically by a stochastic particle method. The stochastic nature of
this method leads to noisy estimates of the thermodynamic quantities one wishes
to sample when the signal is small in comparison to the thermal velocity of the
gas. Recently, Gorji et al have proposed a method which is able to greatly
reduce the variance of the estimators, by creating a correlated stochastic
process which acts as a control variate for the noisy estimates. However, there
are potential difficulties involved when the geometry of the problem is
complex, as the method requires the density to be solved for independently.
  Importance sampling is a variance reduction technique that has already been
shown to successfully reduce the noise in direct simulation Monte Carlo
calculations. In this paper we propose an importance sampling method for the
Fokker-Planck stochastic particle scheme. The method requires minimal change to
the original algorithm, and dramatically reduces the variance of the estimates.
We test the importance sampling scheme on a homogeneous relaxation, planar
Couette flow and a lid-driven-cavity flow, and find that our method is able to
greatly reduce the noise of estimated quantities. Significantly, we find that
as the characteristic speed of the flow decreases, the variance of the noisy
estimators becomes independent of the characteristic speed.
