It is shown that a number of key observations of the Galactic ISM can be understood, if it is treated as a highly compressible and turbulent medium energized predominantly by supernova explosions (and stellar winds). We have performed extensive numerical high resolution 3D hydrodynamical and magnetohydrodynamical simulations with adaptive mesh refinement over sufficiently long time scales to erase memory effects of the initial setup. Our results show, in good agrement with observations, that (i) volume filling factors of the hot medium are modest (typically below 20%), (ii) global pressure is far from uniform due to supersonic (and to some extent superalfvenic) turbulence, (iii) a significant fraction of the mass (about 60%) in the warm neutral medium is in the thermally unstable regime (500 K < T < 5000 K), (iv) the average number density of OVI in absorption is 1.81 10^{-8} cm^{-3}, in excellent agreement with Copernicus and FUSE data, and its distribution is rather clumpy, consistent with its measured dispersion with distance.
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