  We study the time evolution of a large-scale magnetic flux threading an
accretion disk. Induction equation of the mean poloidal field is solved under
the standard viscous disk model. Magnetic flux evolution is controlled by the
two timescales: One is the timescale of the inward advection of the magnetic
flux, tau_{adv}. This is induced by the dragging of the flux by the accreting
gas. The other is the outward diffusion timescale of the magnetic flux
tau_{dif}. We consider diffusion due to the Ohmic resistivity. These timescales
can be significantly different from the disk viscous timescale tau_{disk}. The
behaviors of the magnetic flux evolution is quite different depending on the
magnitude relationship of the timescales tau_{adv}, \tau_{dif}, and tau_{disk}.
The most interesting phenomena occurs when tau_{adv} << tau_{dif}, tau_{disk}.
In such a case, the magnetic flux distribution approaches a quasi-steady
profile much faster than the viscous evolution of the gas disk, and also the
magnetic flux has been tightly bundled to the inner part of the disk. In the
inner part, although the poloidal magnetic field becomes much stronger than the
interstellar magnetic field, the field strength is limited to the maximum value
that is analytically given by our previous work (Okuzumi et al. 2014, ApJ, 785,
127). We also find a condition for that the initial large magnetic flux, which
is a fossil of the magnetic field dragging during the early phase of star
formation, survives for a duration in which significant gas disk evolution
proceeds.
