Numerical simulations of magnetosonic wave formation driven by an expanding cylindrical piston are performed to get better physical insight into the initiation and evolution of large-scale coronal waves. Several very basic initial configurations are employed to analyze intrinsic characteristics of the MHD wave formation that do not depend on specific properties of the environment. It turns out that these simple initial configurations result in piston/wave morphologies and kinematics that reproduce common characteristics of coronal waves. In the initial stage the wave and the expanding source-region cannot be clearly resolved. During the acceleration stage of the source-region inflation, the wave is driven by the piston expansion, so its amplitude and phase-speed increase, whereas the wavefront profile steepens. At a given point, a discontinuity forms in the wavefront profile. The time/distance required for the shock formation is shorter for a more impulsive source-region expansion. After the piston stops, the wave amplitude and phase-speed start decreasing. During the expansion, most of the source region becomes strongly rarified, which reproduces the coronal dimming left behind the eruption. On the other hand, the density increases at the source-region boundary, and stays enhanced even after the expansion stops, which might explain stationary brightenings that are sometimes observed at the edges of the erupted coronal structure. In addition, in the rear of the wave a weak density depletion develops, trailing the wave, which is sometimes observed as weak transient coronal dimming. Finally, we find a well defined relationship between the impulsiveness of the source-region expansion and the wave amplitude and phase speed. The results for the cylindrical piston are also compared with the outcome for a planar wave, to find out how different geometries affect the evolution of the wave.
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