A question of boundary conditions.
 

I wrote a program in Fortran to simulate the pulsatile flow through a straight pipe by solving the Navior-Stokes equations. At the inlet I imposed the velocity profile in the Bessel functions,at the outlet I imposed an zero normal stress condition,and at the wall I considered the velocity to be equal to that of the wall.But I don't know how to give the boundary conditions of the pressure.Can someone help me? Thanks.

Re: A question of boundary conditions.
 

You can dictate a pressure value at the inlet and use zero normal gradient at the exit. Apply global mass conservation at the exit in case you apply dp/dn=0

at the walls you would need to get the pressure conditions from the N-S equations. refer book by anderson et al

Re: A question of boundary conditions.
 

I feel that your boundary condition is not enough at the outlet. You only have the stress BC in normal direction, how about the other directions?

If you don't impose any pressure boundary condition, you can set pressure value at one node anywhere you want.

Re: A question of boundary conditions.
 

Thanks xueying, actually I used the boundary condition at the exit in the zero normal velocity gradient.And what I mean is that I impose an zero normal pressure gradient at the outlet, but I think that the boundary condition isn't enough for pressure, do you thik so? And must I impose the boundary condition for pressure at the inlet?

Re: A question of boundary conditions.
 

Zero normal velocity gradient means fully developed flow, is it right? I don't understand why zero normal velocity gradient means zero normal pressure gradient.

I also use fully developed flow. It is n.\delta v=0 in my code. I can either set pressure there or not, depend on what I want. if we don't have any pressure condition, then I need one relative pressure. In my code, I set pressure zero in the first element.

Re: A question of boundary conditions.
 

Thanks a lot,xueying. Yes, what I mean is fully developed flow. As you said, zero velocity gradient does not mean zero pressure, I used it only because I did not know what the gradient for pressure at the outlet is.But in my code I had to impose the gradient at the exit because I used the finite element method based on velocity correction which was first raised by Kovacs et al.(1991).In the method, it requres imposing the gradient of pressure at the boundary.