I want to assign free outflow as boundary condition. I know that free outflow means stresses + pressure null. But i cannot specify pressure, I must leave it free to develop. Is it enough if I set only stresses equal to zero?
The selection of the outflow condition is strictly depending on the solving algorithm that is being used to give the solution.
For example, if you're using the Simple algorithm, the pressure can not be imposed anywhere in the domain because of the nature of the algorithm.
In substitution, one should impose for example the velocity, the stresses or the null - gradient b.c.
I hope this will be of help for your problem.
If you need more info just contact me.
In compressible flows information is propagated into, out of, and inside the domain along characteristics. So I would recommend you to read the paper
"Boundary conditions for direct simulations of compressible viscous flows"
Poinsot, T. J.; Lele, S. K.
Journal of Computational Physics (ISSN 0021-9991), vol. 101, no. 1, July 1992, p. 104-129.
If one ignores these subtle balances of density, velocity, and pressure at the boundaries artificial effects will be the consequence.
Dear Antonella,
what model equations and what kind of discretization are you using?
For (compressible) Navier-Stokes equations and finite element discretizations, you might consider the work of Rannacher, who is an expert in this field. Or, for finite volume discretizations and large eddy simulation, surely Thierry Poinsot as indicated above by Heiko is an expert.
I have myself been working a bit in CFD using Navier-Stokes and finite elements. In this context, you might do a quick search for the "do nothing" outflow boundary conditions, i.e. gradient of velocity - pressure times outer normal = 0 at the outflow boundary.
The answer depends on the equation of state of the fluid inside. If it's compressible, but the flow is subsonic, and you've specified outflow velocity, then you've already imposed a lot of conditions on the normal derivative of the pressure. (For a moving boundary problem, of course, you can give the pressure, also.) The tangential components of stress do not present computational problems.
The number and type of bc.s depends upon local supersonic or subsonic conditions. I suppose you can work with zero normal derivative for the velocity at the outlet (if it is quite downstream) but if the flow is subsonic you need to fix an energetic condition, for example in terms of pressure. Be carefull that in such case the opposite is at your inlet where you cannot set all BC.s but one condition will come from the interior.
The paper of Poinset and Lele is very good to address your question.
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