Calculation of Laminar Backward-Facing Step Flow With Four Descretization Schemes for The Convection Terms

Abstract

In the present work, the performance of four finite difference formulations for the steady-state, two-dimensional partial differential equations for fluid flows were examined. The finite difference formulations were the: i.) upwind finite difference scheme (UDS) ii.) hybrid central/upwind finite difference scheme (CUDS) iii.) quadratic, upstream-weighted finite difference scheme (QUDS) iv.) hybrid central/skewed-upwind finite difference scheme (CSUDS) The schemes (QUDS) and (CSUDS) proved to be superior to the two former discretization schemes when applied to the convective terms of the fluid flow equations to yield numerical predictions of backward-facing step flows. With both the (QUDS) and the (CSUDS) scheme, grid independence of the flow results was achieved with a largely reduced number of grid points. Also, numerical diffusion, was strongly reduced with both schemes and it is shown in the paper that the results obtained with both the (QUDS) and the (CSUDS) scheme are in close agreement.