We investigate the time evolution of luminous accretion disks around black holes by conducting two-dimensional radiation-hydrodynamic simulations. We adopt the α prescription for the viscosity. The radial-azimuthal component of the viscous stress tensor is assumed to be proportional to the total pressure in the optically thick region and the gas pressure in the optically thin regime. The viscosity parameter, α, is taken to be 0.1. We find the limit-cycle variation in luminosity between high and low states. When we set the mass input rate from the outer disk boundary to be 100L_E/c², the luminosity suddenly rises from 0.3L_E to 2L_E, where L_E is the Eddington luminosity. It decays after retaining the high value for about 40 s. Our numerical results can explain the variability amplitude and duration of the recurrent outbursts observed in microquasar GRS 1915+105. We show that multidimensional effects play an important role in the high-luminosity state. In this state, the outflow is driven by the strong radiation force, and some part of the radiation energy dissipated inside the disk is swallowed by the black hole due to the photon-trapping effects. This trapped luminosity is comparable to the disk luminosity. We also calculate two more cases: one with a much larger accretion rate than the critical value for the instability and the other with the viscous stress tensor being proportional to the gas pressure only, even when the radiation pressure is dominant. We find no quasi-periodic light variations in these cases. This confirms that the limit-cycle behavior found in the simulations is caused by the disk instability.