Implicit solution of the incompressible Navier-Stokes equations on a non-staggered grid

Abstract

This paper presents an implicit procedure for the solution of the incompressible Navier-Stokes equations in primitive variables. The time dependent momentum equations are solved implicitly for the velocity field using the approximate factorization technique. The continuity equation is satisfied at each time step through the solution of a Poisson type equation for the static pressure. A consistent finite-difference scheme which satisfies the compatibility condition using a non-staggered grid is used in the finite difference approximation of the static pressure Poisson equation. The results of the numerical computations in a driven cavity, which are presented for the history of the residues, at several Reynolds numbers using different computational parameters, demonstrate the excellent convergence characteristics of the solution procedure. A stability analysis is conducted for the non-iterative phase and numerical results are presented for a given set of compational parameters. Numerical results obtained for the steady state static pressure in the driven cavity are presented for the first time at Re =1000 using a non-staggered grid, and the steady state velocity, vorticity, and pressure contours at Re = 100, 400, and 1000, are compared with the computational results of other investigators. Additional results using a curvilinear grid are also presented for the flow in a cascade of circular airfoils at Re = 1000.