# How to couple navier-stokes to potential flow in a finite volume solver?

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 March 10, 2015, 11:03 How to couple navier-stokes to potential flow in a finite volume solver? #1 New Member   Nederland Join Date: Mar 2015 Posts: 4 Rep Power: 10 Hello, Does anyone know an efficient way of coupling steady NS equations (or RANS) to potential flow on non-overlapping domains, when both flows are solved by a colocated finite volume method? For transient flows, I found a solution that uses the velocity from the PF as a bc for the NS solver, and the pressure from NS is then used in the transient Bernoulli eq. to update the velocity potential on the interface for the PF solver. For the steady case I tried a kind of pseudo time stepping in the Bernoulli eq but did not manage to get things nice & stable. Any suggestions, references...? Thanks! Philip

 March 26, 2015, 18:22 #2 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,014 Blog Entries: 29 Rep Power: 38 The scalar potential gradient is, actually, a velocity field. Couldn't you use that for the coupling? Just guessing, never tried...

 March 27, 2015, 02:56 #3 New Member   Nederland Join Date: Mar 2015 Posts: 4 Rep Power: 10 Hi, thanks for answering, and yes, you can/should use that. I am now skipping the Bernoulli eq for the coupling, and doing it in a more direct way by only matching the velocities with a deferred-correction method. Matched velocities yield both mass & momentum conservation over the interface - that seems good enough. The steady Bernoulli eq is mainly tricky because if you plug in the pressure (from the NS side) to get an updated velocity/flow potential, the 1/2V.mag^2 term has 2 solutions and taking one of them would probably introduce locking the solution to either in- or outflowing, where you want to leave it free to move from in- to outgoing on the interface, and vv. Ph

 March 27, 2015, 08:19 #4 Member   Alex Join Date: Jan 2014 Posts: 54 Rep Power: 11 Could you solve the potential flow field first, then use the results as a boundary condition for the region where you use N-S? I would think this would work pretty well if you know where your flow field will be potential.

 March 27, 2015, 10:24 #5 Member   Alex Join Date: Jan 2014 Posts: 54 Rep Power: 11 Actually, it just occurred to me there are codes already that do something similar to this. Interactive Boundary Layer Codes (XFoil) is an example), solve the potential field, then employ a boundary layer solver to resolve the flow near the surface. About a year ago I read a thesis where the Cebeci-Smith model was employed to approximate separation. Ill see if I can get the name

 March 27, 2015, 11:05 #6 New Member   Nederland Join Date: Mar 2015 Posts: 4 Rep Power: 10 Ok, would be nice if you could give a reference. I am just looking for a general coupling of Pot Flow with NS, in fact not with a special boundary layer code. The idea is to only use NS where it is necessary (viscous effects) and Pot Flow in the rest. As far as I know (and could find), this is often done when combining BEM with FVM or FEM for free surface flows around ships. Philip

 March 27, 2015, 11:21 #7 Member   Alex Join Date: Jan 2014 Posts: 54 Rep Power: 11 You need to look up interactive boundary methods. They are well documented. Im at work now I cant get yoy anything until later.

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