Multidimensional upwinding for incompressible flows based on characteristics

In this paper, the multidimensional characteristic based upwind scheme (MCB) which has been recently introduced by the authors is applied to two another benchmark problems namely flow in a channel with a backward facing step and two-dimensional steady and unsteady flows past a circular cylinder. Extension of MCB scheme for calculating convective fluxes on non-Cartesian grids is presented here. For the flow over backward facing step, obtained results were compared against well-known experimental data and the results show high accuracy of MCB scheme and faster convergence rate with respect to conventional CB scheme. In the case of flow over circular cylinder, the flow at steady and transient regimes is investigated by MCB scheme. Again, the results obtained by MCB are compared to the other results in the literature and show good agreement with them. Also, rapid convergence rate of MCB was observed in this case too. It is concluded that, the genuinely multidimensional characteristic based (MCB) scheme, has been introduced earlier by the authors, is a robust and powerful scheme for modeling incompressible viscous flows for achieving the high accuracy and remarkable advantage in convergence rate with respect to conventional characteristic based schemes.