Stability of a colocated finite volume scheme for the Navier-Stokes equations

The aim of this article is to describe a colocated finite volume approximation of the incompressible Navier-Stokes equation and study its stability. One of the advantages of colocated finite volume space discretizations over staggered space discretizations is that all the variables share the same location; hence, the possibility to more easily use complex geometries and hierarchical decompositions of the unknowns. The time discretization used in the scheme studied here is a projection method. First, we give the full discretization of the incompressible Navier-Stokes equations, then, we state the stability result and prove it following the methods of Marion and Temam. (C) 2004 Wiley Periodicals, Inc.