OUTFLOW BOUNDARY CONDITIONS FOR TIME DEPENDENT, PERIODIC FLOWS

The issue of outflow boundary conditions arises in numerical experiments. In most cases, it is well known what kind of boundary conditions to impose at the inlet or along the sides of the domain. However, the outflow is almost always unknown as far as boundary consitions is concerned. There is an ongoing discussion about this issue from the 1970's until today. This discussion, though, seems to be old fashioned for steady state flows. Indeed, the availability of immense computational power permits extension of domains until any distortion of the flow due to the outflow can be overcome. For unsteady (periodic) flows, the issue of appropriate boundary conditions will never be overcome, since the periodicity extends to infinity and computational domains are finite. One of the most successful concepts that is being used in the literature at outflows is the so called free boundary condition. Although it has been successfully used for periodic flows, this concept is primarily well known for steady state flows. This is due to the fact the free boundary conditions has not been used in benchmark periodic flows such as the von Karman vortex street in the flow around a circular cylinder at Re = 100 or the Poiseuille-Benard flow in a channel where traveling Bernard roll cells are created. In this work, these two benchmark flows are studied using the concept of the free boundary condition. It is shown, that the flow occurs undisturbed up to the outlfow without any distortion in the interior of the domain. In this way, the important characteristis of the flow (periodocity, calculation of grad coeeficient) are studied without any issue. Any distortion close to the outflow does not propaget upstream of the outflow. The most attractive attribute of the free boundary condition is that requires no assumption at the outflow boundary. In this way, the character of the numerical experiment is unaffected.