Convergence of a Colocated Finite Volume Scheme for the Incompressible Navier-Stokes Equations

摘要

We study a finite volume scheme for the approximation of the incompressible Navier-Stokes equations in two dimensions. It uses a projection (fractional step) method to ensure the incompressibility constraint. The unknowns for the velocity and the pressure are colocated at the center of the cells of a triangular mesh. The discrete operators are consistent and satisfy a discrete inf-sup (Babuska-Brezzi) condition. We state the stability and the convergence of the scheme, and give some numerical results.