Finite-element analysis of incompressible Navier-Stokes equations involving exit pressure boundary conditions

This article presents finite-element solutions for incompressible Navier-Stokes equations in velocity-pressure variables. Specific to this study is the inclusion of pressure boundary conditions into the mixed finite-element formulation. To provide an in-depth analysis of the finite-element model, rigorous derivations have been carried out. The justification for applying the finite-element code to simulate this class of flow problems is presented by solving a problem which is amenable to analytical solution and the backward-facing step benchmark problem. In addition, results for blood flow in a carotid artery are presented to show the applicability of the finite-element code to geometrically more complex problems.