Upcoming wide-field surveys are well suited to studying the growth of galaxy clusters by tracing galaxy and gas accretion along cosmic filaments. We use hydrodynamic simulations of volumes surrounding 324 clusters from The ThreeHundred project to develop a framework for identifying and characterizing these filamentary structures and associating galaxies with them. We define three-dimensional reference filament networks reaching 5R200 based on the underlying gas distribution and quantify their recovery using mock galaxy samples mimicking observations such as those of the WEAVE Wide-Field Cluster Survey. Since massive galaxies trace filaments, they are best recovered by mass-weighting galaxies or imposing a bright limit (e.g. >L*) on their selection. We measure the transverse gas density profile of filaments, derive a characteristic filament radius of ≃ 0.7–1 h−1Mpc, and use this to assign galaxies to filaments. For different filament extraction methods, we find that at R > R200, ∼15–$20{{\ \rm per\ cent}}$ of galaxies with M* > 3 × 109M⊙ are in filaments, increasing to $\sim 60{{\ \rm per\ cent}}$ for galaxies more massive than the Milky Way. The fraction of galaxies in filaments is independent of cluster mass and dynamical state and is a function of cluster-centric distance, increasing from ∼13 per cent at 5R200 to ∼21 per cent at 1.5R200. As a bridge to the design of observational studies, we measure the purity and completeness of different filament galaxy selection strategies. Encouragingly, the overall three-dimensional filament networks and ∼67 per cent of the galaxies associated with them are recovered from two-dimensional galaxy positions.

Galaxy cluster outskirts are described by complex velocity fields induced by diffuse material collapsing towards filaments, gas, and galaxies falling into clusters, and gas shock processes triggered by substructures. A simple scenario that describes the large-scale tidal fields of the cosmic web is not able to fully account for this variety, nor for the differences between gas and collisionless dark matter. We have studied the filamentary structure in zoom-in resimulations centred on 324 clusters from the threehundred project, focusing on differences between dark and baryonic matter. This paper describes the properties of filaments around clusters out to five R200, based on the diffuse filament medium where haloes had been removed. For this, we stack the remaining particles of all simulated volumes to calculate the average profiles of dark matter and gas filaments. We find that filaments increase their thickness closer to nodes and detect signatures of gas turbulence at a distance of ${\sim}2 \rm {{{~h^{-1}\,{\rm Mpc}}}}$ from the cluster. These are absent in dark matter. Both gas and dark matter collapse towards filament spines at a rate of ${\sim}200 \,\rm {km ~ s^{-1}\, h^{-1}}$. We see that gas preferentially enters the cluster as part of filaments, and leaves the cluster centre outside filaments. We further see evidence for an accretion shock just outside the cluster. For dark matter, this preference is less obvious. We argue that this difference is related to the turbulent environment. This indicates that filaments act as highways to fuel the inner regions of clusters with gas and galaxies.