COMPLETE PRESSURE CORRECTION ALGORITHM FOR SOLUTION OF INCOMPRESSIBLENAVIER-STOKES EQUATIONS ON A NONSTAGGERED GRID

When Navier-Stokes equations for incompressible flow are solved on a n onstaggered grid, Be problem of checkerboard prediction of pressure is encountered. So far, this problem has been cured either by evaluating the cell face velocities by the momentum interpolated principle [1] o r by evaluating an effective pressure gradient in the nodal momentum e quations [2]. In this article it is shown that not only are these prac tices unnecessary, they can lead to spurious results when the true pre ssure variation departs considerably from linearity. What is required instead is afresh derivation of the pressure correction equation appro priate for a nonstaggered grid. The pressure correction determined fro m this equation comprises two components: a mass-conserving component and a smoothing component. The former corresponds to the pressure corr ection predicted by a staggered grid procedure, whereas the latter sim ply accounts for the difference between the point value of the pressur e and the cell-averaged value of the pressure. The new pressure correc tion equation facilitates (in a significant way) computer coding of pr ograms written for three-dimensional geometries employing body-fitted curvilinear coordinate grids.