  Galaxy clusters in the Universe occupy the important position of nodes of the
cosmic web. They are connected among them by filaments, elongated structures
composed of dark matter, galaxies, and gas. The connection of galaxy clusters
to filaments is important, as it is related to the process of matter accretion
onto the former. For this reason, investigating the connections to the cosmic
web of massive clusters, especially well known ones for which a lot of
information is available, is a hot topic in astrophysics. In a previous work we
performed an analysis of the filament connections of the Coma cluster of
galaxies, as detected from the observed galaxy distribution. In this work we
resort to a numerical simulation whose initial conditions are constrained to
reproduce the Local Universe, including the region of the Coma cluster to
interpret our observations in an evolutionary context. We detect the filaments
connected to the simulated Coma cluster and perform an accurate comparison with
the cosmic web configuration we detected in observations. We perform an
analysis of the halos' spatial and velocity distributions close to the
filaments in the cluster outskirts. We conclude that, although not
significantly larger than the average, the flux of accreting matter on the
simulated Coma cluster is significantly more collimated close to the filaments
with respect to the general isotropic accretion flux. This paper is the first
example of such a result and the first installment in a series of publications
which will explore the build-up of the Coma cluster system in connection to the
filaments of the cosmic web as a function of redshift.
