An analysis of a covolume method for the stationary navier-stokes equations

Abstract

We introduce a covolume method for approximating the stationary Navier- Stokes equations and analyze the convergence of the covolume approximation. The covolume method uses the primal and dual partitions. The velocity is approximated using nonconforming piecewise linear functions and the pressure piecewise constants. We use an abstract theory to the study of the convergence of the covolume method for the Navier-Stokes equations, which is based on the results of approximation for branches of nonsingular solutions of nonlinear problems presented in [10]. Numerical results using a simple Picard type of iteration for solving the discrete Navier-Stokes equations are provided. © 2009 Academic Publications.