A flow-condition-based interpolation finite element procedure for incompressible fluid flows

A new finite element procedure for the solution of the incompressible Navier–Stokes equations is presented. In the Petrov–Galerkin formulation employed, the velocities are interpolated using the flow conditions over the elements and the pressure is interpolated to satisfy the inf–sup condition for incompressible analysis. Element control volumes are employed to satisfy local mass and momentum conservation (as in finite volume methods), which corresponds to using step functions as weight functions in the finite element method. An important achievement of the discretization scheme is that no artificial parameters are set in the scheme to reach stability for low and high Reynolds (and Péclet) number flows. The solutions of nontrivial test problems are presented to demonstrate the capability and potential of the scheme.