Multifaceted asymmetric radiation from the edges (MARFEs) are regions of high-density and low-temperature plasma observed under certain conditions at the tokamak edge. Such structures are found to form in a natural way on the closed flux surfaces near the X-point in 2D numerical simulations (B2-EIRENE) of the divertor plasmas at high discharge densities. Stable steady-state solutions can be obtained by the conventional edge code if the hydrogen line-radiation opacity is taken into account in the model, both with and without impurity radiation. In addition to extra power losses from the MARFE the detached divertor solution is affected due to (i) reduction of the separatrix temperature and thus plasma pressure; (ii) additional momentum losses due to friction with atoms produced by the recombining plasma of the MARFE.