Fluid dynamical view of pressure checkerboarding problem and smoothing pressure correction on meshes with colocated variables

This paper presents derivation of the pressure correction equation appropriate for colocated grids within the framework of the SIMPLE algorithm. It is shown that checkerboard prediction of pressure can be prevented by employing algebraic smoothing pressure correction [Numer. Heat Transfer, Part B 29 (1996) 441] that is very simple to implement on both the structured as well as unstructured grids. The ability of the smoothing correction (which is shown to be independent of transformations of the system of coordinates) in providing the necessary dissipation is explained and the connection of the former with requirements of the Stokes’s laws is established.