Boundary conditions
 

Hi,

I'm considering a 2D oscillating cylinder (longitudinal direction) and adopt the method which the frame of reference is fixed onto the cylinder.

For the cylinder, I know that the velocity should be u=v=0. Also, the Navier Stokes equation should include an acceleration term, thus

du/dt=(1/Re)(Laplacian u)-dp/dx-udu/dx-vdu/dy-dUo/dt

whereby Uo is the velocity of oscillation.

What I am not clear of is what outer boundary conditions should be used. Can I use the convective boundary condition of du/dt + Udu/dx =0,

or should there be an additional term,

du/dt + Udu/dx - dUo/dt = 0?