The talk Boundary conditions for Navier-Stokes(-like) equations imposed on artificial boundaries: two points of view, by Martin Lanzendörfer, will be held on Monday October 24, 2016 at 9:00 in room K3.
It seems natural to our minds to separate the "inner" and "outer", despite of them being inseparable in essence. In the (computational) fluid dynamics it is often practical to consider the flow problems in a bounded domain. In many cases, there are parts of the domain's boundary that are artificial: not related to any natural physical interface. The choice of boundary conditions to be imposed on artificial boundaries is then a modelling issue, where neither the physics alone nor the mathematical well-posedness analysis alone give conclusive recommendations.
The talk will be shortly motivated by the lubrication flow in a plane slider bearing. Then, we will focus on the inflow and outflow boundary conditions for Navier-Stokes equations in the case that the flow rate is not known a priori. We will discuss one particular set of examples demonstrating the non-uniqueness and the (lack of) stability for the "do-nothing" b.c.'s and the b.c.'s based on prescribed traction. The practical drawbacks of the known alternatives (such as the "directional do-nothing" b.c.'s) will be mentioned as well.