Hi,

I have a quick question regarding implementation of non-reflecting outflow boundaries in a cell-centre code, the method I'm trying is by Giles. My physical condition is a static pressure imposed at the exit, and both the inlet and exit are subsonic. To start I have the following three characteristics (in 1D), where d means delta:

dw1 = drho â€" (1/a^2)*dP, for entropy wave u

dw2 = du + (1/(rho*a))*dP, for acoustic wave u+a

dw3 = du - (1/(rho*a))*dP, for acoustic wave u-a

after Giles and others the amplitude of incoming waves can/are set to zero, therefore at a subsonic exit, dw3=0. I am assuming that I take the value of my imposed exit static pressure (residing in my ghost cell) and take the value of pressure in cell next to the boundary to provide dP. I can then use equation three for dw3 to get du = (1/(rho*a))*dP ?? This may or may not be correct??

From here on in I'm stuck, I need drho, but can't use the other two equations for dw1, and dw2 as I've too many unknowns?!?

Can anybody help me with this? I'm really looking for implementation level details, and the piece of knowledge I'm missing rather than a reference to a paper. I've got loads of those, and all seem to lead me to this point (obviously if the paper does indeed explain the implementation and the missing piece of theory then just as good)

Cheers,

There is a paper in JCP 1992 titled " Boundary conditions for direct simulation of compressible viscous flows" by Poinsot and Lele which has an exhaustive discussion on the different kinds of boundary conditions depending on if the flow is subsonic or supersoni,if pressure is fixed etc.Also another option is the application of the buffer zone of Freund or Energy transfer and annhiliation condition of Visbal.

Many thanks,

actually the paper you refer to is for the LODI relations which are then used to determine all types boundary conditions. This is over kill for my application, and additionally rather hard to implement in finite volume, cell-centred, face based methods. I'm aware of the literature, and decided on this specifically because of it's apparent easy of implementation while being non-reflective.

I'd really welcome peoples comments/help who understand the specific questions and method (Giles' approach) which I posed in my first post - and hopefully can provide answers to them.

Cheers,

Then you might want to look the the buffer zone method of freund.I have been using that for a while and it has been pretty effective.It is given by

df/dt =H -sigma*f-U*(df/dx)

where sigma=sigma0*[(x-xstart)/(xend-xstart)]^beta U=U0*{(x-xstart)/(xend-xstart)}^beta sigma0=1.2/dx,U0=1-2,beta=2-3

The non reflecting boundary condition of giles may produce reflections if your problem takes long runs to become periodic.I have tried the characteristic boundary condition of thompson and it worked fine for simple cases and was not able to absorb the outgoing energy for long time runs.

Many thanks,

again, Giles' method is the specific method I want to use - I'd like to get this thread back on the track of my original post.

Could anybody with specific experience of Giles' method provide me with some info regarding my questions in the original post. I would very much appreciate comments surrounding those points, in particular why dw2 seems redundant at the exit boundary, and dw1 is not usable because I can't close it at the exit boundary....

Cheers,

Why not extrapolate the characteristic quantities from the interior of the flowfield for dw1 and dw1, and then use that information, along with the fact that dw3 is zero, to solve for the variations of drho, dp, and du on the boundaries?

Ok, now your exact post is the point I don't understand, it's in all the papers, phased as you put it, but I just can't get how to implement it?

Could you explain, for example, what I need to do for the following characteristic? How can I extrapolate this from the interior, or rather I think my problem is, what do I extrapolate from the interior?

dw1 = drho â€" (1/a^2)*dP

I'd really appreciate your help,

Cheers,

You can integrate the equations to get

S = p/rho^g R1= u/2 + a/(g-1) R2= u/2 - a/(g-1)

where g = gamma = ratio of specific heats.

These are constant along characteristics u, u+a and u-a

For subsonic exit face, take S and R1 from the last cell (or extrapolate for greater accuracy) and p from the exit pressure. You have three equations and three unknowns.

Hi,

Many thanks, actually these are the Riemann Invariants based boundary conditions, they are reflective boundary conditions, and should be used only for far field boundaries. They additionally assume constant entropy and enforce far-field inlet conditions at the exit, again I don't want this. The current approach that I'm discussing with Ag is anon-reflective boundary condition and is slightly more advanced, which can be applied in the near field and is what I require for my application.

Many thanks though,

Yes, it assumes constant entropy. It is not reflective.

with the greatest of respect, there is a large body of literature that would disagree with you. Riemann invariant based bc are reflective, and should be used only for far fields. This is why there are approaches based on characteristic in which only the incoming wave amplitudes are zeroed.

I would try the classic case of a Gaussian pressure plus in your domain with two Riemann invariant outlet bc, you'll see the reflection of the waves, which would pass out unreflected using either the approach I am asking about or the method sighted by Harish in which the LODI relations are used to close the problem, see his reference to Lele's paper.

Anyway, I wish to use the approach of Giles for my own reasons not Riemann Invariant bc's, buffer zone's or PML's, as outlined in my original post, and I would like to get some clarification on the points I made in response to Ag's post (hopefully from Ag and others).

Ok Ag I've had sometime to think about your points,

so say we do this, considering the subsonic outlet only with an imposed static pressure.

setting dw3=0, and using an upstream point in relation to the point on the boundary, one can compute dw1 and dw2, I then using zero order extrapolation set dw1 and dw2 at the boundary to these values.

rearranging the equations one gets (in terms of knowns):

du = dw2/2

dp = dw2*rho*a/2

drho = dw1 + dw2*rho/(2*a)

Thus far I have not had cause to use the value of my imposed exit static pressure...this is kind of where I'm going with this.

I then wish to update the values in the ghost cell to the right of the exit boundary (cell-centred method). How do I do this? Do I for instance say that the ghost cell pressure is the exit imposed static pressure + dp just computed, or???

This is kind of where I get lost. Would one set the density at the exit to be for instance the current value of the density in the ghost cell + drho??

I hope you see my confusion.

Cheers,

It's been a while since I implemented non-reflective conditions, but if you fix the boundary pressure doesn't that defeat the purpose of trying to absorb any pressure pulse?

Hi,

Sorry for not replying before. I agree that fixing the pressure will do as you say, but I'm confident that I need to use the exit pressure in some manner, this is the part I'm not sure about...? (Of course these arguments and similar for imposed density and velocity at the inlet using the same approach)

If I simply say that the boundary value for pressure is the current value plus dP, then at no point have I supplied an exit boundary condition, which seems wrong to me....

any chance you could dig out your implementation and have a look?? I feel that I'm kind of close...

Many thanks,