  This paper presents simulations of the 2d model developed by Poth\'erat at al
(\emph{J. Fluid Mech}, 2000) for MHD flows between two planes with a strong
transverse homogeneous and steady magnetic field, accounting for moderate
inertial effects in Hartmann layers. We first show analytically how the
additional terms in the equations of motion accounting for inertia, soften
velocity gradients in the horizontal plane, and then we implement the model on
a code to carry out numerical simulations to be compared with available
experimental results. This comparison shows that the new model can give very
accurate results as long as the Hartmann layer remains laminar. Both
experimental velocity profiles and global angular momentum measurements are
closely recovered, and local and global Ekman recirculations are shown to alter
significantly the aspect of the flow as well as the global dissipation.
