Solution of transport equations on unstructured meshes with cell-centered colocated variables. Part I: Discretization

This paper describes discretization of transport equations on unstructured meshes with cell-centered colocated variables. The problem of zig-zag pressure prediction is eliminated by introducing smoothing pressure correction derived by Date [A.W. Date, Complete pressure correction algorithm for solution of incompressible Navier-Stokes equations on a non-staggered grid, Numer. Heat Transfer, Part B 29 (1995) 441-458]. The finite-volume discretization is carried out in a structured grid like manner by invoking a special line-structure to evaluate convective-diffusive transport across the cell-faces.