A comparative study of finite volume pressure-correction projection methods on co-located grid arrangements

Incompressible time dependent flows have many important applications and numerous studies have been carried out to numerically solve the governing equations of such flows. Among them, projection methods have been widely studied and used in the context of finite element/difference methods. In most of these studies staggered grids were employed to simplify the implementation of pressure boundary conditions. In this paper non-incremental, standard incremental and rotational incremental pressure-correction projection methods are implemented on co-located grids in the context of finite volume method. Implicit, semi-implicit and Crank-Nicolson schemes have been used for the time integration. Transient version of the momentum interpolation method is used in the discretization process to prevent numerical oscillations in the pressure field. Lid driven cavity and backward facing step flows are used as test problems. It is found that the standard incremental pressure-correction scheme is numerically more stable and provides more accurate results even with larger time steps as compared to other pressure-correction methods.