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We address here the discretization of the momentum convection operator forfluid flow simulations on 2D triangular and quadrangular meshes and 3Dpolyhedral meshes containing hexahedra, tetrahedra, prisms and pyramids. Thefinite volume scheme that we use for the full Euler equations is based on astaggered discretization: the density unknowns are associated with a primalmesh, whereas the velocity unknowns are associated with a "fictive" dual mesh.Accordingly, the convection operator of the mass balance equation is derived onthe primal mesh, while the the convection operator of the momentum balanceequation is discretized on the dual mesh. To avoid any hazardous interpolationof the unknowns on a possibly ill-defined dual mesh, the mass fluxes of themomentum convection operator are computed from the mass fluxes of the massbalance equation, so as to ensure the stability of the resulting operator. Acoherent reconstruction of these dual fluxes is possible, based only on thekind of considered polygonal or polyhedral cell, and not on each cell itself.Moreover, we show that this process still yields a consistent convectionoperator in the Lax-Wendroff sense, that is, if a sequence of piecewiseconstant functions is supposed to converge to a a given limit, then the weakform of the corresponding discrete convection operator converges to the weakform of the continuous operator applied to this limit. The derived discreteconvection operator applies to both constant and variable density flows and maythus be implemented in a scheme for incompressible or compressible flows.Numerical tests are performed for the Euler equations on several types of mesh,including hybrid meshes, and show the excellent performance of the method.

A staggered scheme for the compressible Euler equations on general 3D meshes