IMPLEMENTATION OF A FREE-BOUNDARY CONDITION TO NAVIER-STOKES EQUATIONS

Numerical simulation of a fluid flow involves the specification of bou ndary conditions along all or part of the boundary. Designs a means of handling outflow boundary conditions for the incompressible Navier-St okes equations. Addresses through-flow problems involving the specific ation of out-flow conditions at the synthetic boundary. This outflow b oundary condition is applicable to a developing flow problem. The unde rlying objectives behind designing the boundary condition at the trunc ated boundary are three-fold, namely: matching with Navier-Stokes equa tions inside the domain; taking both non-linear and diffusive contribu tions into account; and ensuring the discrete divergence-free conditio n. 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 su rface 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 appr oach zero. With the convergent property accommodated in the present mi xed finite element analysis, the task remains to simply improve the ac curacy. Demonstrates the capability of the proposed non-linear outflow boundary conditions through several bench-mark tests.