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In this work in collaboration with F.Filbet,we construct a hierarchy of hybrid numerical methods for the Boltzmann equation,based on moment realizability.We present hybrid schemes where the hydrodynamic part is given either by the compressible Euler or Navier-Stokes equations,or even with more general models,such as the Burnett system.We present numerical simulations in both 1 and 2 dimensions of physical space,and 3 of velocity.