On the finite element modelling of viscous-convective flow

The efficiencies of the Ritz-Galerkin and least squares finite element methods in the modeling of viscous convective flows are examined. Relationships between the Ritz-Galerkin and least squares methods are discussed, and it is found that both the discrete least squares and least squares methods represent least squares extensions of the Galerkin procedure. The accuracy and stability of the methods are analyzed for the solution of the basic convective transport equation for the momentum-vorticity transport of viscous convective flow, for which unrealistic oscillations of the solution may be obtained. It is found that the appropriate discretization of the flow region is the necessary condition for the application of the finite element methods considered, and the least squares method is characterized by high numerical stability. Numerical results of the analysis are presented, and it is concluded that the use of upwind schemes is not necessary if the flow region can be satisfactorily discretized.