Pressure-velocity coupling algorithm on non-orthogonal non-staggered grid

In this paper, a new numerical procedure is proposed for the steady flow of a viscous, incompressible fluid based on SIMPLER algorithm on a non-orthogonal non-staggered grid, together with Cartesian velocity components as dependent variables in the momentum equations. The main feature of the algorithm is that the pressure and pressure correction equations are obtained by explicitly treating pressure cross-derivatives terms in interface contravariant velocities. A collocated arrangement of variables is introduced on numerical grids, and the cell face velocities are calculated by the momentum interpolation. It is proved that this algorithm can be effectively used to simulate fluid flow and heat transfer in complex geometry, by the validation calculation of flow inside branching channel.