We study the two-dimensional, time-dependent hydrodynamics of radiation-driven winds from luminous accretion disks in which the radiation force is mediated primar- ily by spectral lines. We assume the disk is flat, Keplerian, geometrically thin, and optically thick, radiating as an ensemble of blackbodies according to the -disk pre- scription. The effect of a radiant central star is included both in modifying the radial temperature profile of the disk, and in providing a contribution to the driving radi- ation field. Angle-adaptive integration techniques are needed to achieve an accurate representation of the driving force near the surface of the disk. Our hydrodynamic calculations use non-uniform grids to resolve both the subsonic acceleration zone near the disk, and the large-scale global structure of the supersonic wind. We find that line-driven disk winds are produced only when the effective luminos- ity of the disk (i.e. the luminosity of the disk times the maximum value of the force multiplier associated with the line-driving force) exceeds the Eddington limit. If the dominant contribution to the total radiation field comes from the disk, then we find the outflow is intrinsically unsteady and characterised by large amplitude velocity and density fluctuations. Both infall and outflow can occur in different regions of the wind at the same time. The cause of this behaviour is the difference in the variation with height of the vertical components of gravity and radiation force: the former increases while the latter is nearly constant. On the other hand, if the total luminosity of the system is dominated by the central star, then the outflow is steady. In either case, we find the two-dimensional structure of the wind consists of a dense, slow outflow, typi- cally confined to angles within 45 degrees of the equatorial plane, that is bounded on the polar side by a high-velocity, lower density stream. The flow geometry is controlled largely by the geometry of the radiation field – a brighter disk/star produces a more polar/equatorial wind. Global properties such as the total mass loss rate and terminal velocity depend more on the system luminosity and are insensitive to geometry. The mass loss rate is a strong function of the effective Eddington luminosity; less than one there is virtually no wind at all, whereas above one the mass loss rate in the wind scales with the effective Eddington luminosity as a power law with index 1.5. Matter is fed into the fast wind from within a few stellar radii of the central star. Our solutions agree qualitatively with the kinematics of outflows in CV systems inferred from spectroscopic observations. We predict that low luminosity systems may display unsteady behavior in wind-formed spectral lines. Our study also has applica- tion to winds from active galactic nuclei and from high mass YSOs.