  Low-frequency rotating spokes are obtained in a cross-field discharge plasma
using two-dimensional numerical simulations. A particle-fluid hybrid model is
used to model the plasma flow in a configuration similar to a Hall thruster. It
has been reported that the drift-diffusion approximation for an electron fluid
results in an ill-conditioned matrix when solving for the potential because of
the differences in the electron mobilities across the magnetic field and in the
direction of the E$\times$B drift. In this paper, we employ a hyperbolic
approach that enables stable calculation, namely, better iterative convergence
of the electron fluid model. Our simulation results show a coherent rotating
structure propagating in the E$\times$B direction with a phase velocity of
2,500 m/s, which agrees with experimental data. The phase velocity obtained
from the numerical simulations shows good agreement with that predicted by the
dispersion relation of the gradient drift instability.
