Genuinely multidimensional characteristic-based scheme for incompressible flows

This paper presents a novel multidimensional characteristic-based (MCB) upwind method for the solution of incompressible Navier-Stokes equations. As opposed to the conventional characteristic-based (CB) schemes, it is genuinely multidimensional in that the local characteristic paths, along which information is propagated, are used. For the first time, the multidimensional characteristic structure of incompressible flows modified by artificial compressibility is extracted and used to construct an inherent multidimensional upwind scheme. The new proposed MCB scheme in conjunction with the finite-volume discretization is employed to model the convective fluxes. Using this formulation, the steady two-dimensional incompressible flow in a lid-driven cavity is solved for a wide range of Reynolds numbers. It was found that the new proposed scheme presents more accurate results than the conventional CB scheme in both their first- and second-order counterparts in the case of cavity flow. Also, results obtained with second-order MCB scheme in some cases are more accurate than the central scheme that in turn provides exact second-order discretization in this grid. With this inherent upwinding technique for evaluating convective fluxes at cell interfaces, 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 the CB scheme that is found to exhibit substantial delays in convergence reported in the literature. The results obtained using new proposed scheme are in good agreement with the standard benchmark solutions in the literature. Copyright (C) 2007 John Wiley & Sons, Ltd.