A Finite Difference Galerkin Formulation for the Incompressible Navier-Stokes Equations

The development of a new computational method for solving the incompressible Navier-Stokes equations in primitive variable form is presented. It is found that certain finite difference approximations for these equations can be transformed into an equivalent system which efficiently determines the discrete velocity field and which completely eliminates the pressure. Two such difference schemes for two dimensional problems are examined and some preliminary numerical results are discussed for the steady driven cavity problem.