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.
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