Some convergence problems in the numerical solution of the navier-stokes equations

Abstract

The convergence of numerical solutions of the Navier-Stokes equations for steady two-dimensional flow is examined and convergence criteria for both ψ and ζ are obtained for a rectangular mesh. The criterion for ψ is shown to be less stringent, in general, than that for ζ. A new method of solution, based on the process used to obtain the convergence criteria, is derived. This method widens the range over which convergence can be obtained and can also be used to accelerate the convergence rate.