  To study the full formation and evolution history of galaxy clusters and
their population, high resolution simulations of the latter are flourishing.
However comparing observed clusters to the simulated ones on a one-to-one basis
to refine the models and theories down to the details is non trivial. The large
variety of clusters limits the comparisons between observed and numerical
clusters. Simulations resembling the local Universe down to the cluster scales
permit pushing the limit. Simulated and observed clusters can be matched on a
one-to-one basis for direct comparisons provided that clusters are well
reproduced besides being in the proper large scale environment. Comparing
random and local-Universe like simulations obtained with differently grouped
observational catalogs of peculiar velocities, this paper shows that the
grouping scheme used to remove non-linear motions in the catalogs that
constrain the simulations affects the quality of the numerical clusters. With a
less aggressive grouping scheme - galaxies still falling onto clusters are
preserved - combined with a bias minimization scheme, the mass of the dark
matter halos, simulacra for 5 local clusters - Virgo, Centaurus, Coma, Hydra
and Perseus - is increased by 39% closing the gap with observational mass
estimates. Simulacra are found on average in 89% of the simulations, an
increase of 5% with respect to the previous grouping scheme. The only exception
is Perseus. Since the Perseus-Pisces region is not well covered by the used
peculiar velocity catalog, the latest release let us foresee a better
simulacrum for Perseus in a near future.
