Implementation of a free boundary condition to Navier-Stokes equations

Numerical simulation of a fluid flow involves the specification of boundary conditions along all or part of the boundary. Designs a means of handling outflow boundary conditions for the incompressible Navier-Stokes equations. Addresses through-flow problems involving the specification of out-flow conditions at the synthetic boundary. This outflow boundary condition is applicable to a developing flow problem. The underlying objectives behind designing the boundary condition at the truncated boundary are three-fold, namely: matching with Navier-Stokes equations inside the domain; taking both non-linear and diffusive contributions into account; and ensuring the discrete divergence-free condition. In order to meet these requirements, follows the concept of a free boundary condition by taking the outflow nodal values of u, v and p as unknowns, which are coupled with the interior unknowns through the surface integrals in the momentum equations. The computed solutions can be legitimately regarded as solutions to conservation equations under consideration when both components of the surface traction vector approach zero. With the convergent property accommodated in the present mixed finite element analysis, the task remains to simply improve the accuracy. Demonstrates the capability of the proposed non-linear outflow boundary conditions through several bench-mark tests.