  Determinations of the shear viscosity of trapped ultracold gases suffer from
systematic, uncontrolled uncertainties related to the treatment of the dilute
part of the gas cloud. In this work we present an analysis of expansion
experiments based on a new method, anisotropic fluid dynamics, that
interpolates between Navier-Stokes fluid dynamics at the center of the cloud
and ballistic behavior in the dilute corona. We validate the method using a
comparison between anisotropic fluid dynamics and numerical solutions of the
Boltzmann equation. We then apply anisotropic fluid dynamics to the expansion
data reported by Cao et al. In the high temperature limit we find
$\eta=0.282(mT)^{3/2}$, which agrees within about 5\% with the theoretical
prediction $\eta=0.269(mT)^{3/2}$.
