[Bdew8556]

Hi all,

I'm using the far field pressure condition in Fluent.
All fine there. I understand qualitatively it's meant to simulate conditions far away from the object and that it's usually used in external aerodynamics.

I'm curious what exactly it is setting mathematically?
I see something about the Riemann invariant.

Can anyone elaborate?

Brett

[LuckyTran]

The short answer is it is equivalent to a pressure inlet or pressure outlet boundary condition. The difference is, the pressure being used has the same characteristic (the same Riemann invariant) as the farfield conditions being specified. In other words, you calculate the Riemann invariants of the farfield condition, and then choose the local pressure that matches this invariant.

[Bdew8556]

interesting....

could you describe what the Reimann invariants are?

[FMDenaro]

Riemann invariants are a proper combination of variables that remains constant along its characteristic lines.
However, the existence of such invariants is constrained by the hyphotheses of omo-entropic flows. Even in case of iso-entropic flows they are no longer invariant.
This is a fundamental topic in any textbook of Gasdynamics.

[sbaffini]

One can generalize the concept to systems of hyperbolic equations, where the Riemann invariants are the independent variables for which you solve the system after a diagonalization of the flux jacobian.

In the present specific case they are the variables that, under proper assumptions, can be naturally upwinded, because they either enter or leave the domain according to the wave structure of the problem.

In more layman terms, it is not just the pressure, temperature or velocity that you can assign at inlet/outlet and be sure that it isn't dependent from what happens in the domain, but a more complex variable which is a combination of all the above. Such variables, the riemann invariants, under proper conditions, can be shown to either leave or enter the domain, so that they can either be assigned (where they enter) or extrapolated from the interior (where they leave)