SUMMARYWe develop in this paper a discretization for the convection term in variable density unstationary Navier-Stokes equations, which applies to low-order non-conforming finite element approximations (the so-called Crouzeix-Raviart or Rannacher-Turek elements). This discretization is built by a finite volume technique based on a dual mesh. It is shown to enjoy an L 2 stability property, which may be seen as a discrete counterpart of the kinetic energy conservation identity. In addition, numerical experiments confirm the robustness and the accuracy of this approximation; in particular, in L 2 norm, second-order space convergence for the velocity and first-order space convergence for the pressure are observed.

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