Stability of a finite volume scheme for the incompressible fluids

Abstract

We introduce a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection method to deal with the incompressibility constraint. We show that the differential operators in the Navier-Stokes equations and their discrete counterparts share similar properties. In particular we state an inf-sup (Babuska-Brezzi) condition. Using these properties we infer the stability of the scheme.