Boundary condition on curved boundary
 

Hey,

I have written a vorticity stream function code for flow in a cavity. The code produces nice results compared to the literature. With the addition of a cylinder to the cavity the results become very different compared to commercial software (I have not checked against literature, but I have tried both Fluent and COMSOL).

This makes me wonder about the boundary condition for vorticity on the cylinder wall. Is it correct to assume similar boundary condition on the curved boundary as on vertical/horizontal boundaries - as long as the derivatives are calculated from nodes in the wall normal direction?

I also attach a simulation with Re=100 (based on the cavity, not the cylinder), where you can see the behavior.

Thanks!

Update:

So after pulling my hair with this for some time I realized that the vorticity boundary condition was ok. The problem was the stream function specification on the internal boundary (cylinder). It needs to be constant, but what constant value should it have? I now use the normal derivative of the stream function (i.e. the tangential velocity) as specification of the stream function value at the wall. The trick was to calculate this for one node on the cylinder wall and then set all other nodes on the cylinder wall equal to that value.

The results are much better as can be seen in the attached image.