International Journal of Industrial Engineering & Production Management

 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 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 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.