Static Pressure Inlet - Static Pressure Outlet
 

Hello,

My FDM code simulates Backward Facing Step flow when I use conventional BCs such as defining velocity profile at inlet and fully developed condition at outlet. I have validated the results and it seems functioning correctly.

However, when I want to impose a pressure-pressure condition (both static), it only converges when a zero-gradient condition is selected for inlet. When I try to use mass balance to update inlet normal velocity at each iteration, the solution eventually blows up. I am integrating outflow and use the mean velocity as a uniform inlet velocity.

Also I am interested to know if there is any difference to use momentum balance and mass balance to update inlet normal velocity.

Has anyone faced this problem before? I appreciate your help:)

Solution will not converge when Neumann boundary condition is used for a variable at all boundaries. Static pressure-static pressure boundary condition has no meaning, one of the boundary condition should contain velocity. When four equations are solved four variables should be specified as Dirichlet boundary condition.

Well, you should provide more details...
1) are you using Neumann at walls and Dirichlet at inflow and outflow? what about the pressure difference ?
2) are you using staggered or colocated grid?
3) how do you discretize the pressure equation?

Thanks Duri and Filippo for your comments. I am using a collocated explicit MacCormack (predictor-corrector) scheme for incompressible flow with pseudo-compressibility coupling for pressure. The BCs that converge for pressure-pressure are listed below:

@inlet: p=p_in , du/dx=0 , dv/dx=0
@outlet: p=p_out , du/dx=0, dv/dx=0
@walls: dp/dy=0 (or the extended version) , u=0, v=0

The BCs that won't converge:

@inlet: p=p_in , u=U_in , v=0
@outlet: p=p_out , du/dx=0, dv/dx=0
@walls: dp/dy=0 (or the extended version) , u=0, v=0

I find "U_in" from mass conservation at the end of each iteration and update it.
I have used pressure-pressure condition in CFX without zero-gradient condition so many times, so there should be a way for convergence.

The error is that you can not prescribe both pressure and velocity as Dirichlet bc

Thanks Filippo. I did not know about this. Could you kindly introduce me a book or paper that discusses what kind of Dirichlet and Neumann conditions go well together?

Ideally your both conditions should not converge. If it converges it might be for wrong value. Because for given static pressure difference in unchoked flow mass flow is not unique, it is determined by inlet or exit velocity. Both of your boundary condition doesn't fix the velocity at either of the boundaries. So, I expect velocity would keep on change on both boundaries unless there is choking. Some were you need to fix either mass flow or velocity or total pressure. Try to solve simple bernouli's equation with above conditions you can't.

https://www.researchgate.net/publica..._viscous_flows

Duri I am solving for incompressible flow.

compressible or incompressible???