  In the blowout regime of plasma wakefield acceleration (PWFA), which is the
most relevant configuration for current and future applications and
experiments, the plasma flow that is excited by the ultra-relativistic drive
beam is highly nonlinear. Thus, fast and accurate simulations codes are
indispensable tools in the study of this extremely important problem. We have
developed a novel algorithm that deals with the propagation of axisymmetric
bunches of otherwise arbitrary profile through a cold plasma of uniform
density. In contrast to the existing PWFA simulation tools, our code PLEBS
(PLasma-Electron Beam Simulations) uses a new computational scheme which
ensures that the transverse and longitudinal directions are completely
decoupled---a feature which significantly enhances the speed and robustness of
the new method. Our numerical results are benchmarked against the QuickPic code
and excellent agreement is established between the two approaches. Moreover,
our new technique provides a very convenient framework for studying issues such
as beam loading and short-range wakefields within the plasma cavity.
