Jonas Holdeman 
March 19, 2013 11:08 
open boundary condition
1 Attachment(s)
I thought about this a little more and did a Google search on open boundary conditions. Most of the hits seemed to involve atmospheric or oceanic flows and radiation, and the methods seem mostly heuristic. My examples involve a specific method, but perhaps there are general considerations.
Quote:
Originally Posted by andreachan
(Post 414942)
Do you also know the mathematical description of such boundary condition?

In my example, mass is strongly conserved. This is done (in 2D) by using modified Hermite elements for the stream function, where the derivative terms are the velocity (it could be called a stream function  velocity method). The velocity elements are the curl of the stream function element and hence are strongly divergencefree. I think it might work when truncating the mesh through a recirculation bubble because any fluid outflow carried out through an open face, say by its momentum, must be replaced by an equal inflow. Perhaps the condition needed is that mass conservation must be strong and independent of what is happening at the outflow.
In my case, the equations for the nodes on the exit face are only partially assembled because here are no elements outside. This may be called a "do nothing" boundary condition. I am not sure why it works, but it does. Any mathematicians out there?
This open condition has further utility. Consider flow over a cylinder. One usually uses a mesh wide enough that the effects of truncation of the space might be neglected. Usually one has to compromise between computational work and accuracy. But suppose you leave the top and bottom of the mesh open as well. Then the fluid could expand outside the mesh near the cylinder, and then reentering downstream, reducing the influence of truncation without additional work. This is shown for Re=50 in the figure, where the top, bottom and right end are open, but net flow through the top and bottom constrained to be zero.
