  Particle-In-Cell (PIC) simulations of relativistic flowing plasmas are of key
interest to several fields of physics (including e.g. laser-wakefield
acceleration, when viewed in a Lorentz-boosted frame), but remain sometimes
infeasible due to the well-known numerical Cherenkov instability (NCI). In this
article, we show that, for a plasma drifting at a uniform relativistic
velocity, the NCI can be eliminated by simply integrating the PIC equations in
Galilean coordinates that follow the plasma (also sometimes known as comoving
coordinates) within a spectral analytical framework. The elimination of the NCI
is verified empirically and confirmed by a theoretical analysis of the
instability. Moreover, it is shown that this method is applicable both to
Cartesian geometry and to cylindrical geometry with azimuthal Fourier
decomposition.
