A Robust Hybrid Staggered/Collocated Mesh Scheme for CFD on Skewed Meshes

In this study, a finite-volume computational fluid dynamics (CFD) technique for application on skewed meshes using staggered pressure nodes is proposed. The method is based on the derivation of a momentum equation for the cell face velocities from appropriately discretised momentum equations in the two cells surrounding the cell face with the driving pressure difference pertaining to the staggered adjacent nodes. In this way, a staggered mesh-like method is obtained that would prevent the occurrence of oscillatory behaviour in pressure or velocity fields. The cell-face velocities are then forced to obey continuity via an equation for pressure akin to other standard CFD schemes. This article describes the formulation of the cell-face momentum equation as well as the way the nodal velocity is reconstructed from the surrounding cell-face velocities. The method is demonstrated to recover the advantages of the PISO solution algorithm that were diminished in implementations in collocated schemes. It is also validated on a reference two-dimensional, steady viscous flow case on both rectangular and skewed meshes to verify its accuracy. It is then applied to the case of an unsteady vortex-shedding flow past a square obstacle, on both rectangular and skewed meshes, and the results are compared with a solution obtained from a collocated method as well as with an experimental value of the Strouhal number.