Resolution of the 2D Navier-Stokes equations in velocity-vorticity form by means of an influence matrix technique

Abstract

An influence matrix technique is proposed to enforce both the continuity equation and the definition of the vorticity in the treatment of the 2D incompressible Navier-Stokes equations. It is shown and supported by numerical experiments that at each time step the divergence is actually equal to zero within machine accuracy. The same result is obtained for the definition of the vorticity.