Finite element solution of the 3D compressible Navier-Stokes equations by a velocity-vorticity method

This paper presents an alternative formulation to the primitive variable form of the Navier-Stokes equations. The approach is based on the use of the velocity and vorticity variables as a logical extension of the stream function-vorticity method which is quite effective for two-dimensional flows. Second-order equations are obtained for the variables and discretization is through a weak-Galerkin finite element method, followed by Newton linearization. The velocity and vorticity components are solved simultaneously by a direct solver. The scheme is demonstrated for two-dimensional and three-dimensional incompressible and subsonic internal enclosed flow problems.