Cross-sections along the equatorial plane of the density in log scale (left column) and of the radial velocity (right column). The top panels show the flux rope with ζ = 15 evolving in the minimum activity configuration, while the bottom panels correspond to the simulation with ζ = 9 in the maximum activity scenario. In the density panels, some magnetic field lines crossing a sphere of radius 1.5 R_⊙ located at x = −16 R_⊙ are also displayed. Each color corresponds to one field line. A virtual satellite was placed at 21.5 R_⊙ (X = −21.5 R_⊙, Y = 0, Z = 0) and is shown as a white sphere. The shape of the sheath is delimited by an ellipse in the density panels. In both solar wind configurations, a sheath is ahead of the flux rope, which is consistent with the observations. When the initial speed of the flux ropes is too high, there are nonphysical high-speed streams in the wake of flux rope legs.