We present two sets of grid-based hydrodynamical simulations of high-velocity clouds (HVCs) traveling through the diffuse, hot Galactic halo. These HI clouds have been suggested to provide fuel for ongoing star formation in the Galactic disk. The first set of models is best described as a wind-tunnel experiment in which the HVC is exposed to a wind of constant density and velocity. In the second set of models we follow the trajectory of the HVC on its way through an isothermal hydrostatic halo towards the disk. Thus, we cover the two extremes of possible HVC trajectories. The resulting cloud morphologies exhibit a pronounced head-tail structure, with a leading dense cold core and a warm diffuse tail. Morphologies and velocity differences between head and tail are consistent with observations. For typical cloud velocities and halo densities, clouds with H{small{I}} masses $< 10^{4.5}$ M$_odot$ will lose their H{small{I}} content within 10 kpc or less. Their remnants may contribute to a population of warm ionized gas clouds in the hot coronal gas, and they may eventually be integrated in the warm ionized Galactic disk. Some of the (still over-dense, but now slow) material might recool, forming intermediate or low velocity clouds close to the Galactic disk. Given our simulation parameters and the limitation set by numerical resolution, we argue that the derived disruption distances are strong upper limits.
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