2D velocity-vorticity viscous incompressible flows

Abstract

The 2D unsteady Navier-Stokes equations in its velocity-vorticity formulation, after time discretization, leads to a nonlinear elliptic system which may be solved by iterative methods; however, decoupling the nonlinear vorticity equation from the vorticity in the velocity equations by linear interpolation, a direct method is applied, allowing the vorticity equation to be linear. Steady state convergent flows from the un–regularized unit driven cavity problem, which causes recirculation because of the nonzero boundary condition on the top wall, are reported for Reynolds numbers Re, 400 ≤ Re ≤ 4000.