An efficient solution method for incompressible N-S equations using non-orthogonal collocated grid

An e$cient strategy for the solution of N-S Equations using collocated, non-orthogonal grids is presented. The governing equations have been discretized in the physical plane itself without co-ordinate transformation, thereby retaining the lucidity of the basic "nite volume method. The non-orthogonal terms and QUICK type corrections for the convective terms in the momentum equations are treated explicitly, while the other terms are taken in implicit form. In the pressure correction equation, the non-orthogonal terms have been dropped altogether. The discretized equations have been solved by the preconditioned conjugate gradient square method. The speci"c combination of above steps has resulted in better convergence properties as compared to those of existing algorithms, even for highly skewed grids. The scheme has been validated against benchmark solutions such as lid-driven #ow in square and skewed cavities and experimental results of #ow over a single cylinder. Its applicability has also been illustrated for #ow through a bank of staggered cylinders, with anti-symmetric inlet and outlet boundary conditions