  In this work we describe the dynamics of a highly anisotropic system
undergoing boost-invariant longitudinal and azimuthally symmetric radial
expansion (Gubser flow) for arbitrary shear viscosity to entropy density ratio.
We derive the equations of motion of dissipative anisotropic hydrodynamics by
applying to this situation the moments method recently derived by Moln\'ar et
al. (MNR) [1,2], based on an expansion around an arbitrary anisotropic
one-particle distribution function. One requires an additional evolution
equation in order to close the conservation laws. This is achieved by selecting
the relaxation equation for the longitudinal pressure with a suitable Landau
matching condition. As a result one obtains two coupled differential equations
for the energy density and the longitudinal pressure which respect the
$SO(3)_q\otimes SO(1,1)\otimes Z_2$ symmetry of the Gubser flow in the deSitter
space. These equations are solved numerically and compared with the predictions
of the recently found exact solution of the relaxation-time-approximation
Boltzmann equation subject to the same flow. We also compare our numerical
results with other fluid dynamical models. We observe that the MNR description
of anisotropic fluid dynamics reproduces the space-time evolution of the system
than all other currently known hydrodynamical approaches.
