Computation of Incompressible Viscous Flows, Using a Novel Multi-dimensional Characteristic Based Upwind Scheme

In this paper, a novel multi-dimensional characteristic based upwind scheme for incompressible viscous flows is presented. Unlike conventional characteristic based (CB) schemes, which use one-dimensional characteristic relations, the proposed scheme takes into account the physical multi-dimensional characteristic relations. For the first time, the multi-dimensional characteristic structure of incompressible flows, modified by artificial compressibility, is extracted. The present MCB (multi-dimensional characteristic based) scheme, in conjunction with the finite-volume discretization, is employed to model convective fluxes. This MCB scheme is applied to benchmark incompressible internal and external flows, namely lid driven cavity flow and two-dimensional flow past a circular cylinder. It was found that the proposed scheme presents more accurate results than the conventional CB scheme in both their first and second order counterparts. Using this inherent upwinding technique, no artificial viscosity is required, even at high Reynolds numbers. Another remarkable advantage of MCB scheme lies in its faster convergence rate with respect to CB scheme, which is found to exhibit substantial delays in convergence. Our results are in good agreements when compared to standard benchmark data.