  Large-scale magnetic fields play a vital role in determining the angular
momentum transport and generating jets/outflows in the accreting systems, yet
their origin remains poorly understood. We focus on radiatively inefficient
accretion flows (RIAFs) around the black holes (BHs), and conduct
three-dimensional general-relativistic magnetohydrodynamic (GRMHD) simulations
using the Athena++ code. We first re-confirm that the MRI dynamo in the RIAF
alone does not spontaneously form a magnetically arrested disk (MAD), conducive
for strong jet formation. We next investigate the other possibility, where the
large-scale magnetic fields are advected inward from external sources (e.g. the
companion star in X-ray binaries, magnetized ambient medium in AGNs). Although
the actual configuration of the external fields could be complex and uncertain,
they are likely to be closed. As a first study, we treat them as closed field
loops of different sizes, shapes and field strengths. Unlike earlier studies of
flux transport, where magnetic flux is injected in the initial laminar flow, we
injected the magnetic field loops in the quasi-stationary turbulent RIAF in
inflow equilibrium and followed their evolution. We found that a substantial
fraction ($\sim15\%-40\%$) of the flux injected at the large radii reaches the
BH with a weak dependence on the loop parameters except when the loops are
injected at high latitudes, away from the mid-plane. Relatively high efficiency
of flux transport observed in our study hints that a MAD might be formed
relatively easily close to the BH, provided that a source of the large-scale
field exists at the larger radii.
