In order to solve Navier-Stokes equations on a moving domain or with simple schemes, non body fitted meshes are chosen. The goal of this work is to introduce difficulties encountered with such a choice and to show a way to overcome them. The first part is devoted to the presentation of a modified boundary condition to take into account the fact that physical walls are approached by the mesh. A second part deals with the algorithm to solve bifluid Navier-Stokes equations. Then, bifluid flows with surface tension are considered and some applications follow. As we are concerned with computational cost, we show how fast, a mesh generation and a Poisson multigrid solver (AGMG) are. Keywords: Navier-Stokes equations, bifluid flows.