ELLIPTICITY, ACCURACY, AND CONVERGENCE OF THE DISCRETE NAVIER-STOKES EQUATIONS

The introduction into the continuity equation of additional terms to recover grid-scale ellipticity, for the Navier-Stokes equations discretised on a non-staggered mesh, results in an increase in the discretisation error. The introduced error is a combination of the additional truncation error and a false source resulting from the inconsistent construction of the conservation equations used in the finite volume scheme considered. The false source error component is removed by constructing the conservation terms consistently, while the additional truncation error is shown to be of the same order as the leading order truncation error associated with the unmodified equations. A method of reducing the magnitude of the additional terms, thereby reducing the additional error, is considered. It is shown that although this does reduce the magnitude of the error it also reduces the ellipticity of the equations and leads to slower convergence. (C) 1994 Academic Press, Inc.