  At ~16-17Mpc from us, the Virgo cluster is a formidable source of information
to study cluster formation and galaxy evolution in rich environments. Several
observationally-driven formation scenarios arose within the past decade to
explain the properties of galaxies that entered the cluster recently and the
nature of the last significant merger that the cluster underwent. Confirming
these scenarios requires extremely faithful numerical counterparts of the
cluster. This paper presents the first CLONE, Constrained LOcal and Nesting
Environment, simulation of the Virgo cluster within a ~15Mpc radius sphere.
This cosmological hydrodynamical simulation, with feedback from supernovae and
active galactic nuclei, with a ~3x10^7Msun dark matter particle mass and a
minimum cell size of 350pc in the zoom region, reproduces Virgo within its
large scale environment unlike a random cluster simulation. Overall the
distribution of the simulated galaxy population matches the observed one
including M87. The simulated cluster formation reveals exquisite agreements
with observationally-driven scenarios: within the last Gigayear, about 300
small galaxies (M*>10^7Msun) entered the cluster, most of them within the last
500Myr. The last significant merger event occurred about 2 Gigayears ago: a
group with a tenth of the mass of today's cluster entered from the far side as
viewed from the Milky Way. This excellent numerical replica of Virgo will
permit studying different galaxy type evolution (jellyfish, backsplash, etc.)
as well as feedback phenomena in the cluster core via unbiased comparisons
between simulated and observed galaxies and hot gas phase profiles to
understand this great physics laboratory.
