  Fluid simulations, which are considerably simpler and faster, have been
employed to study the behavior of the wakefield driven by a relativistic rigid
beam in a 2-D cold plasma. When the transverse dimensions of the beam are
chosen to be much larger than its longitudinal extent, a good agreement with
our previous 1-D results [\textcolor{red}{\it Physics of Plasmas 22, 073109
(2015)}] are observed for both under-dense and over-dense beams. When the beam
is overdense and its transverse extent is smaller or close to the longitudinal
extension, the 2-D blow-out structure, observed in PIC simulations and
analytically modeled by Lu et al. [\textcolor{red}{\it Phys. Rev. Lett., 96,
165002 (2006)}] are recovered. For quantitative assessment of particle
acceleration in such a wake potential structure test electrons are employed. It
is shown that the maximum energy gained by the test electrons placed at the
back of the driver beam of energy $\sim 28.5$ GeV, reaches up to $2.6$ GeV in a
10 cm long plasma. These observations are consistent with the experimental
results presented in ref. [\textcolor{red}{\it Phys. Rev. Lett. 95, 054802
(2005)}]. It is also demonstrated that the energy gained by the test electrons
get doubled ($\sim 5.2$ GeV) when the test particles are placed near the axis
at the end of the first blowout structure.
