Help: On oscillating circular cylinder
 

I am trying to solve 2D flow past a transversely oscillating cylinder in cross flow in non inertial frame of reference. In this non inertial frame, the mesh size is fixed and the whole domain will oscillate and move with the flow.Boundary conditions I have used are as follows:

At inlet:
u=1-(2*pi*As*fe*Cos(2*pi*fe*t))
v=0
Here, fe=Frequency of vibration, As=Amplitude, t=time

Top and bottom walls: (Free slip BC)

v=o
du/dy=o

At cylinder surface: u=v=0(no slip)

Outlet:

Fully developed: du/dx=dv/dx=0

Here in non inertial frame of reference I have added one source term in u-momentum equation as:

du/dt + u(du/dx) + v(du/dy) = -(dp/dx) + (1/Re)*grad^2(u)+ (4*(pi^2)*(fe^2)*As*Sin(2*pi*fe*t))

At outlet I have used presuure=0

Iam stucking with that "what will be the boundary conditions of pressue at all the planes?" As because I have to stick with outlet pressue =0, for traction free exit.

Are the boundary conditions I am using true? Or any modifications required?

I will be so greatful if some one extends hands to suggest me a wayout.

Thanks in advance for your time to read the whole writeup and kind cooperation.
Regards
Sandip

Answer to the quarey
 

Dear Friends,

Thank you for giving your precious time to view the post on oscillating cylinder.After two weeks of continuous thinking and literature survey I have resolved the problem on pressure boundary conditions. Though the situation is non inertial frame of reference, the boundary conditions of pressure will be similar as inertial frame of reference. Specifically, the spatial gradient of pressure will be zero at all places, except at outlet, where Dirichlet boundary condition of pressure has to be imposed by zero value.
Now, I have started getting results!

Hope this information will be helpful for those who are working on similar type of problem.

Regards

Sandip