Circumplanetary disks (CPDs) control the growth of planets, supply material for satellites to form, and provide observational signatures of young forming planets. We have carried out two dimensional hydrodynamical simulations with radiative cooling to study CPDs, and suggested a new mechanism to drive the disk accretion. Two spiral shocks are present in CPDs, excited by the central star. We find that spiral shocks can at least contribute to, if not dominate the angular momentum transport and energy dissipation in CPDs. Meanwhile, dissipation and heating by spiral shocks have a positive feedback on shock-driven accretion itself. As the disk is heated up by spiral shocks, the shocks become more open, leading to more efficient angular momentum transport. This shock driven accretion is, on the other hand, unsteady on a timescale of months/years due to production and destruction of vortices in disks. After being averaged over time, a quasi-steady accretion is reached from the planets Hill radius all the way to the planet surface, and the disk $alpha$-coefficient characterizing angular momentum transport due to spiral shocks is $sim$0.001-0.02. The disk surface density ranges from 10 to 1000 g cm$^{-2}$ in our simulations, which is at least 3 orders of magnitude smaller than the minimum mass sub-nebula model used to study satellite formation; instead it is more consistent with the gas-starved satellite formation model. Finally, we calculate the millimeter flux emitted by CPDs at ALMA and EVLA wavelength bands and predict the flux for several recently discovered CPD candidates, which suggests that ALMA is capable of discovering these accreting CPDs.
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