  We present a series of high-resolution sunspot simulations that cover a time
span of up to 100 hours. The simulation domain extends about 18 Mm in depth
beneath the photosphere and 98 Mm horizontally. We use open boundary conditions
that do not maintain the initial field structure against decay driven by
convective motions. We consider two setups: A sunspot simulation with penumbra,
and a "naked-spot" simulation in which we removed the penumbra after 20 hours
through a change in the magnetic top boundary condition. While the sunspot has
an Evershed outflow of 3-4 km/s, the naked spot is surrounded by an inflow of
1-2 km/s in close proximity. However, both spots are surrounded by an outflow
on larger scales with a few 100 m/s flow speed in the photosphere. While the
sunspot has almost constant magnetic flux content for the simulated time span
of 3-4 days, the naked spot decays steadily at a rate of $10^{21}$ Mx/day. A
region with reduced downflow filling factor, which is more extended for the
sunspot, surrounds both spots. The absence of downflows perturbs the
upflow/downflow massflux balance and leads to a large-scale radially
overturning flow system, the photospheric component of this flow is to the
observable moat flow. The reduction of the downflow filling factor also
inhibits submergence of magnetic field in the proximity of the spots, which
stabilizes them against decay. While this effect is present for both spots, it
is more pronounced for the sunspot and explains the almost stationary magnetic
flux content.
