Complete pressure correction algorithm for solution of incompressible Navier-Stokes equations on a nonstaggered grid

When Navier-Stokes equations for incompressible flow are solved on a nonstaggered 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] or by evaluating an effective pressure gradient in the nodal momentum equations [2]. In this article it is shown that not only are these practices unnecessary, they can lead to spurious results when the true pressure variation departs considerably from linearity. What is required instead is afresh derivation of the pressure correction equation appropriate for a nonstaggered grid. The pressure correction determined from this equation comprises two components: a mass-conserving component and a smoothing component. The former corresponds to the pressure correction predicted by a staggered grid procedure, whereas the latter simply accounts for the difference between the point value of the pressure and the cell-averaged value of the pressure. The new pressure correction equation facilitates (in a significant way) computer coding of programs written for three-dimensional geometries employing body-fitted curvilinear coordinate grids.