Multidimensional Characteristic Based Scheme for the Solution of Incompressible Driven Cavity Flow

In this research, a new multidimensional characteristic based upwind scheme for the solution of incompressible Navier-Stokes equations is presented. The incompressible flow equations have been coupled each other by the aid of artificial compressibility method. Unlike to the traditional characteristic based (CB) schemes, the present scheme is genuinely multidimensional in that the local characteristic paths, along which information is propagated, are used. For the first time, the multidimensional characteristics of incompressible flows along with artificial compressibility is extracted and used to construct an inherent multidimensional upwind scheme. The new proposed MCB (multidimensional characteristic based) scheme in conjunction with the finite-volume discretization is employed to model the convective fluxes. Using this formulation, the steady twodimensional 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 conventional CB shceme 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 is more accurate than central scheme which 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 CB scheme which is found to exhibit substantial delays in convergence reported in the literature. The results obtained using new proposed shceme are in good agreement with standard benchmark solutions in the literature. ƶƈŴƄƯ ŽŚsřźŝ ƽŶƘŝŶƴģ ŢsŵLJŚŝ ƁƹŹ Ʈĩřźţ ƱŚƿźū ƪǀƬŰţ ƽřźŝ ŚƷ ƵźƠů ƪųřŵ źƿŸěŚƳ ƱŚǀƯżƯŻ ŹŚǀƯŚĩ Î  s ƽƺƋŹ ƪǀƗŚưsř Ŷǀ Ï ƹ ƽŵŻźƟ Ŷưůř Ð ƵŶǀĪģ ƶƈŴƄƯ ƽŚƴŞƯ źŝ ƪƯŚĩ ƽŶƘŝƹŵ ŢsŵLJŚŝ ŶƿŶū ƁƹŹ Ĩƿ ƢǀƤŰţ Ʋƿř Źŵ šLJŵŚƘƯ ƽŶƘŝŶƴģ ƽŚƷ źƿƹŚƳ źƿŸěŚƳ Ʈĩřźţ Ţsř ƵŶƃ ƶŗřŹř žĩƺŤsř ƾƗƺƴƈƯ ƽźƿŸě Ʈĩřźţ ƁƹŹ Żř ƵŵŚƠŤsř Śŝ źƿŸěŚƳ Ʈĩřźţ šLJŵŚƘƯ ƩƺƇƹ ŲƿŹŚţ ÐÍ Ñ ÕÐ Ŝƿƺƈţ ŲƿŹŚţ ÎÑ Ó ÕÓ ƱŚǀƯżƯŻ ŹŚǀƯŚĩ żƿźŞţ Ŷůřƹ ƾƯLjsř ŵřŻō ƵŚĮƄƳřŵ ĨǀƳŚĪƯ ƾsŶƴƸƯ Ƶƹźĭ ƾsŶƴƸƯ ƹ ƾƴƟ ƵŶĪƄƳřŵ ƾưƬƗ šŚǀƷ ƺƌƗ [email protected] źŤĩŵ ƽƺƋŹ ƪǀƗŚưsř Ŷǀs ƴƟ ƵŶĪƄƳřŵ ŹŚƿŵŚŤsř żƿźŞţ ƵŚĮƄƳřŵ ĨǀƳŚĪƯ ƾsŶƴƸƯ ƹ ƾ [email protected] źŤĩŵ ƽŵŻźƟ Ŷưůř  żƿźŞţ ƵŚĮƄƳřŵ ĨǀƳŚĪƯ ƾsŶƴƸƯ ƹ ƾƴƟ ƵŶĪƄƳřŵ ŹŚƿŵŚŤsř [email protected] K. Zamzamian Mechanical Engineering Department, Islamic Azad Univeristy Tabriz Branch [email protected] S. E. Razavi School of Mechanical Engineering, Univeristy of Tabriz [email protected] A. Farzadi School of Mechanical Engineering, University of Tabriz [email protected] id11577984 pdfMachine by Broadgun Software a great PDF writer! a great PDF creator! http://www.pdfmachine.com http://www.broadgun.com