The edge and scrape-off layer (SOL) plasma of the inter-ELM phase of an H-mode discharge from the TCV tokamak is modeled with the transport code SolEdge2D-EIRENE (Bufferand et al. Nuclear Fusion 55 (2015)). The numerical simulations, in presence and in absence of C impurities sputtered from the first wall, are presented and compared with the experiments, finding an overall good agreement. The application of the standard two-point model to the simulation results leads to an apparent momentum gain along the divertor leg. A two-fluid two-point model featuring thermally decoupled ions and electrons is introduced and applied to the simulation results, overcoming this apparent discrepancy.