This talk will be devoted to the usage of new discretization schemes on polyhedral meshes in an industrial context. These discretizations called CDO [1, 2] (Compatible Discrete Operator) or Hybrid High Order [3,4] (HHO) schemes have been recently implemented in Code Saturne [5]. Code Saturne is an open-source code developed at EDF R&D aiming at simulating single-phase flows. First, the advantages of robust polyhedral discretizations will be recalled. Then, the underpinning principles of CDO schemes will be presented as well as some applications: diffusion equations, transport problems, groundwater flows or the discretization of the Stokes equations. High Performance Computing (HPC) aspects will be also discussed as it is an essential feature in an industrial context either to address complex and large computational domains or to get a quick answer. Some highlights on the main outlooks will be given to conclude.[-]