Outflow Conditions for the Navier-Stokes Equations with Skew-Symmetric Formulation of the Convective Term

摘要

The classical do-nothing condition is very often prescribed at outflow boundaries for fluid dynamical problems. However, it has a severe drawback in the context of the Navier-Stokes equations, because not even existence of weak solutions can be shown. The reason is that this boundary condition does not exhibit any control about inflow across such boundaries. This has also severe impact onto the stability of numerical algorithms for flows at higher Reynolds number. A modification of this boundary condition is one possibility to circumvent these drawbacks. This paper addresses such modifications in the context of the skew-symmetric formulation of the convective term. Moreover, we introduce a parameter which gives the possibility to downsize possible inflow even more and to enhance the stability further. Numerical examples illustrate the effectiveness of the approach.