Galaxy clusters in local Universe simulations without density
  constraints: a long uphill struggle
  Galaxy clusters are excellent cosmological probes provided that their
formation and evolution within the large scale environment are precisely
understood. Therefore studies with simulated galaxy clusters have flourished.
However detailed comparisons between simulated and observed clusters and their
population - the galaxies - are complicated by the diversity of clusters and
their surrounding environment. An original way initiated by Bertschinger as
early as 1987, to legitimize the one-to-one comparison exercise down to the
details, is to produce simulations constrained to resemble the cluster under
study within its large scale environment. Subsequently several methods have
emerged to produce simulations that look like the local Universe. This paper
highlights one of these methods and its essential steps to get simulations that
not only resemble the local Large Scale Structure but also that host the local
clusters. It includes a new modeling of the radial peculiar velocity
uncertainties to remove the observed correlation between the decreases of the
simulated cluster masses and of the amount of data used as constraints with the
distance from us. This method has the particularity to use solely radial
peculiar velocities as constraints: no additional density constraints are
required to get local cluster simulacra. The new resulting simulations host
dark matter halos that match the most prominent local clusters such as Coma.
Zoom-in simulations of the latter and of a volume larger than the 30 Mpc/h
radius inner sphere become now possible to study local clusters and their
effects. Mapping the local Sunyaev-Zel'dovich and Sachs-Wolfe effects can
follow.
