Hi, everyone:

I do DNS of free jets, but I am not satisfied with the Outflow Boundary Conditions (OBCs) applied in my work, which always do not allow large vortex structures going through the outflow boundary fluently. Would anyone here please recommend a proper OBC to me? Many thanks for this.

Yours,

Jun Xia

For an incompressible flow a convective boundary condition should work: du_i/dt + U du_i/dx = 0. Make sure that the convective velocity U is always positive (and quite large if you still have problems at the outflow)

Tom

Thanks, Tom. Sorry, I do not describe the question clearly. I simulated a compressible (subsonic) free jet and have tried several outflow boundary conditions, but the results are not so good.

Jun

Well, I guess that you know about the work of Freund & Lele or Pitsch (Stanford) in this field.

Tom

Hi,

have you tried to impose non reflective boundary conditions, so that all the waves/perturbations can escape the computational domain without any trouble? This is done by imposing the boundary conditions on the charactersitics of the flow (in 1D these are the Rieman invariants). I know in numerical astrophysics many are simulating jets in the compressible regime and get trouble with reflection at the open boundary. The best way to treat that is to have non-reflective boundary conditions or transmitting boundary conditions.

See e.g. Givoli, 1991, Journal of Computational Physics, no.94, page 1 (review paper).

Patrick

The numerical method you use in this respect is kind of important too. What are you using? Look at Grinstein JCP 94 for a good discussion on open outflow BC's for compressible turbulent flows.

Guus

In this context, it is also worthwhile pointing out that codes based on parabolized Navier Stokes solvers (like FCT, CCCT etc.) seem less problematic for simulation of near field jets. I say this based on observation since I have not worked PNS codes.

For other types of compressible solver, outflow BC is indeed a problem unless you extend the domain far downstream so that the flow at the outflow end of the domain is (relatively) convection dominated. The velocity perturbations due to small vortex structures are small compared to the average convective flow speed. In my experience with jet simulations, you need to extend the domain out (axially) atleast to 40 diameters so that the near field is unaffected by the outflow BC. COmputing unsteady flow in such a huge domain can be very expensive especially if one uses an explicit code like most LES codes but the expense seems to be necessary.

I do not think you can have a true non-reflecting BC in multi-dimensional CFD codes. Even the codes are based on characteristics, they are not genuinely multi-dimensional. There has been some interest a few years ago in developing genuinely multi-dimensional flux-split schemes but I do know how far they have come. Some one more informed can shed more light on this work.

As to Freund' work, do you mean the following paper:

Title: Numerical simulation of a Mach 1.92 turbulent jet and its sound field Author: Freund, J.B.;Lele, S.K.;Moin, P. Source: AIAA Journal v 38 n 11 Nov 2000. p 2023-2031

Would you please recommend Pitsch's paper to me, which I do not know. Very thanks.

Thanks. I use the 4-order compact finite difference scheme in space discretization, and 4-order explicit Runge-Kutta schemes in time advancement.

Thanks. Would you please recommend an article on your former work about jet simulation to me?

With regard to the flux-split method, do you mean the PML (Perfectly Matched Layer) method, i.e. adding a daming item in the end of the equations, like

u_t = (original terms) - sigma*(u - u_damp) ?

I think Convective BC is a reasonable one, though you need some experience in coupling the BC with the interior scheme to ensure numerical stability. The 4th-order compact scheme alone might encouter instability, especially mathed with a compex boundary conditions.

By flux split methods, I mean the methods based on right and left characteristics (Riemann solvers) at each cell face like the van Leer method. While methods based on van Leer scheme and Roe schemes work pretty well in 1-D (shock tube problems) they have problems when extended to multi-dimensional flows (carbuncle phenomena, artificial entropy decrease which is physically impossible). While each of these problems has been fixed (althoughly not all of them perfectly), the root cause remains the fact that you are extending 1-D characteristics based method to 2D/3D. Why is this extension such a problem when straight forward finite difference, finite element type method can be extended easily from 1-D to 2-D or 3-D. It is because these methods (van Leer, Roe schemes etc.) are inherently non-linear. The solutions are obtained from a Riemann problem using Godunov (type) methods instead of straight forward discretization and can be spatially/temporally discontinuous. Hence they do not fit in well with the multi-dimensional Taylor series expansions (need for extension to multi-dimensions and higher orders) which are based on a certain degree of smoothness in the solution.

The last I have seen on finite difference is a compressible mixing layer simulation by Lui and Lele (AIAA-2001-0291). In this paper the Poinsot Lele BC is applied (JCP92) with temporal damping and an artificial convective term, i.e. one tries to get the flow towards a laminar state in a buffer region in which the solution is not worth much.

[Nishu]

Hi Kalyan,

Do you have any code related to 1D Riemann problem?
Please send me at babuu.nishu@gmail.com
I need it for my research

[jed]

Are you familiar with the "no boundary condition" outflow condition? Some relevant papers:

@article{papanastasiou1992nob,
  title={{A new outflow boundary condition}},
  author={Papanastasiou, T.C. and Malamataris, N. and Ellwood, K.R.J.},
  journal={International Journal for Numerical Methods in Fluids},
  volume={14},
  number={5},
  pages={587--608},
  year={1992},
  publisher={John Wiley \& Sons, Ltd}
}
@article{griffiths1997nbc,
  title={{The ``no boundary condition'' outflow boundary condition}},
  author={Griffiths, D.F.},
  journal={International Journal for Numerical Methods in Fluids},
  volume={24},
  pages={393--411},
  year={1997}
}
@article{renardy1997inb,
  title={{Imposing ``no'' boundary condition at outflow: Why does it work?}},
  author={Renardy, M.},
  journal={International Journal for Numerical Methods in Fluids},
  volume={24},
  number={4},
  pages={413--417},
  year={1997}
}

[Ford Prefect]

Originally Posted by Nishu

Hi Kalyan,

Do you have any code related to 1D Riemann problem?
Please send me at babuu.nishu@gmail.com
I need it for my research

Amazing job digging up tons of out-of-date threads Nishu... I suggest you start a new thread instead with all your requests for different codes that you need in your research.

[Nishu]

hmmmm okay!