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Observations of disk galaxies at z~2 have demonstrated that turbulence driven by gravitational instability can dominate the energetics of the disk. GIDGET is a 1D simulation code, which we have made publicly available, that economically evolves these galaxies from z~2 to z~0 on a single CPU in a matter of minutes, tracking column density, metallicity, and velocity dispersions of gaseous and multiple stellar components. We include an H$_2$ regulated star formation law and the effects of stellar heating by transient spiral structure. We use this code to demonstrate a possible explanation for the existence of a thin and thick disk stellar population and the age-velocity dispersion correlation of stars in the solar neighborhood: the high velocity dispersion of gas in disks at z~2 decreases along with the cosmological accretion rate, while at lower redshift, the dynamically colder gas forms the low velocity dispersion stars of the thin disk.