MUSCL Discretization for the Fluid Flow Convection Operator on Staggered Meshes

We propose in this paper a second order discretization of the momentum convection operator for fluid flow simulation on staggered quadrangular or hexahedral meshes. The velocity is approximated by the Rannacher-Turek finite element. The implemented MUSCL-like approach is of algebraic type, in the sense that the limitation procedure does not invoke any slope reconstruction, and is independent from the geometry of the cells. The derived discrete convection operator applies both to constant or variable density flows; we perform here numerical tests for the barotropic and incompressible Navier-Stokes equations.