Analysis of the Steady Navier-Stokes Equations Based on Green’s Function Approach

Abstract

An iterative-integral scheme based on transformation of the Navier-Stokes and continuity equations into integral equations is developed to the steady two-dimensional, viscous incompressible flows in terms of stream function and vorticity. Integral representations of the stream function and vorticity are obtained by use of Green’s functions. An integral equation for the boundary vorticity is derived with these representations. The recirculating flow, occuring inside a rectangular cavity by the steady movement of one of its walls, is computed. Numerical results are obtained for Reynolds numbers R of 0, 32, 64 and 100. This approach has the advantage of getting direct solutions at R=0 and rapid convergent solutions at other Reynolds numbers.