I'm currently solving incompressible Navier-Stokes system of equations with periodic flow and high viscosity.

Is there any outlet boundary types that avoids the reflection of flow from the outlet back into the computational domain? (Neumann is not sufficient).


Left: $u = C sin (\alpha y + \beta t) + u_0$

Top: open

Bot: wall

Right: open

  • 2
    $\begingroup$ Have a look at complex absorbing potentials. $\endgroup$
    – davidhigh
    Sep 19, 2021 at 22:53
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    $\begingroup$ Can you write down your PDE? $\endgroup$
    – nicoguaro
    Sep 19, 2021 at 23:02
  • 3
    $\begingroup$ It crucially depends on what your PDE is. You probably want to state the model you're using for your flow. $\endgroup$ Sep 19, 2021 at 23:06
  • 2
    $\begingroup$ If you have periodic inlet it means that the (velocity) function is periodic in your domain, so it should be the same that you get in the outlet, doesn't it? $\endgroup$
    – nicoguaro
    Sep 20, 2021 at 20:06
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    $\begingroup$ I give up. You only provided half of the information requested. You don't say what "open boundary" is supposed to mean, you don't say what "wall" is supposed to mean mathematically, you don't show a picture, and you provide a boundary condition for the left boundary that only provides a scalar when the N-S equations require you to provide the full velocity vector. People here can't be expected to keep asking questions if you want to get an answer to your post. $\endgroup$ Sep 21, 2021 at 4:17

1 Answer 1


Even if it is not completely physical in some computational FV codes like OpenFOAM exist something called "inletOutlet" boundary condition that make the speed 0 at the boundary when it assumes negative values (or opposite to the sign of your outlet condition). You can find an explanation here and here. Even if it can be a solution, I suggest you to analyse again the physics of your problem and probably one better solution would be to use a longer domain and standard Neumann.

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