Dear All,

I am investigating the possiblilty of performing LES calcs with a compressible NS solver, using ;

2nd order central difference for convective terms with an explicit Jameson 4th/2nd dissipation scheme

does anyone have experience of such a solver for LES? If so, how did you get on and is there any useful tips you could give me.

Thanks Dave Hunt

-- Dr David L Hunt (Senior Project Supervisor)

*************************** * email: dhunt@ara.co.uk * * tel: +44 (0)1234 350681 * * fax: +44 (0)1234 328584 * * int: 4406 * ***************************

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Manton Lane, Bedford, England, UK, MK41 7PF

Hi,

I've been using a second-order CD on convection and either Crank-Nicholson or implicit backward differencing in time in an FVM flow solver for LES and the results are just fine. There is a lot of people who will say that "they would not be comfortable with such numerics", but I disagree. There is a bunch of published papers with this code and I'll be happy to provide references.

Hrv

Dear Dr. Hrvoje Jasak, I'm a Ph.D. student at Lund Institute of Technology (finishing in September 2000). I developed a parallel LES solver on unstructured grids (tetrahedral-cells), using Residual Distribution scheme approach. The flow solver is second order both in space and time (I use a dual time stepping, so there is no need for a mass matrix inversion-my code is cell vertex based). As you mentioned, there are people in the LES community who will complain about these second order discretization. I would appreciate very much if you could send to me also those references about the code you are using. I want to cite them as references of similar work in my thesis.

Thank you very much! Doru

Hi,

I think Michael Breuer has some papers about this subject.

see http://www.lstm.uni-erlangen.de/~breuer/

There are papers that you can download !

As for LES, I also only uses 2 order schemes in both time and space, and it works fine.

I have not investigated if one could save some grid points if I was using higher order shemes.

Any comment ?

Regards

Jens Chr.

Dear Jens,

The scheme I used so far is second order in space & time. To be more exact it is second order implicit in time (using a Jameson dual time stepping approach to avoid inverting a mass matrix - which may be always necessary when you have a cell-vertex data structure and you wanna have second order accuracy in time) and second order hybrid central-upwind scheme for the convective term (central second order for the diffusive term). The discretization scheme is based on a Residual distribution scheme. Its advantages: - accurate - compact (cell based computations) - easy to parallelize (I two week I had first time my code running parallel) - extendible to higher order (I already succeded to obtain third order accuracy by using a close to FEM approach) maintaining the same compact stencil. This is possible, while using this dual time step approach and using a special reconstruction method. The idea and the proof will be presented in a invited lecture at CSCC 2000 Vouliagmeni, Greece. Fourth order is underway... About the second order accuracy, I read in a paper (I'll try to find it and to send it to you) from CTR Stanford, that from their studies, second order central schemes provide better statistics than higher order upwind schemes. High order schemes can be easy obtain with finite differences and regular geometries (in a box for instance). As I developed this code for LES in complex geometries, RD approach seems to me more interesting. It has a great potential anyway!

Comments are wellcome!

Best regards,

Doru

PS. I suppose that there will be peoples from the LES community who will not agree that second order accuracy my be enough for LES.. Yes, but higher order accuracy for complex geometries is comming!

Dear Jens,

In

Mittal, R. and Moin, P., Suitability of Upwind Biased Finite differences Schemes for LES of Turbulent Flows, AIAA J., Vol. 35, no 8, (1997), pp. 1415-1417,

It is shown that "a second order central difference solution of the flow around a cylinder produces better velocity power spectra, as compared with experiments, than the high order upwind schemes, but the lower order statistics appear to be comparable". Thus, "the high order upwind schemes do not appear to be justified due to their increased cost". This was the conclusion of people from CTR.

In my work, probably because I could not have such fine- resolved LES simulations, I needed to use a hybrid central-upwind approach (say, a lot of central and a little upwind ) to stabilize my computations. The upwind scheme is still second order. The turbulent channel flow looks fine, the results in complex applications (see channel with a flame holder, etc.) look also OK (i.e. The mean is perfectly fine and the error in the first order statistics is of the same order as the measurement error-well, second order statistics I don't have for that complex application... but I'm sure the results are not that OK ). So, I think in the future I'll look for that compact RD approach that I wrote in my previous posting.

I will sincerely welcome any comments!

Sincerely,

Doru

It is interesting to see how many people are using 2nd order central difference schemes. My specific problem seems to be to do with dissipation levels. I have been using the 4th order Jameson explicit dissipation model to stabilize my solution. However, if this is too high, I loose most of my turbulence. If it is too low, then I get odd-even decoupling leading to negative pressures. I have not found a balance that works.

I'm currently trying the 2nd order dissipation with pressure switch. This is giving better results.

Does anyone have experience of using a solver with explicit Jameson type dissipation? Or has anyone modified this type of methodology succesfully?

I am interested to hear any insights into how people's second order C.D. methods are stabilising their solutions without dissipating the turbulent field.

Dave

Please forgive my ignorance on the subject matter.

I have two questions:

(1) What is generally the reason for proposing to use higher order schemes? Is it for resolving the convective term or the SGS stress term more accurately?

(2) For the case with complex (or even simple) geometries, do people use adaptive gridding with LES? If not, why?

Thanks in advance

Adrin Gharakhani

Hello Adrin,

No problem, I'm not a specialist in LES. It happens that I implemented a LES code for my Ph.D. degree, with three SGS models in it, which simply works well. Though, most of my work is CFD.

Here are my answers:

(1) What is generally the reason for proposing to use higher order schemes? Is it for resolving the convective term or the SGS stress term more accurately?

Usually people appreciate the order of accuracy of the scheme after the leading term in the truncation error. You my think that the SGS term is of order delta (grid size) squared (just because it has a delta squared in front of it). Then, if you don't want to mask the influence of your SGS term by too much dissipation you have to have higher than two order of accuracy. But, it is also true that the numerical dissipation of the scheme can act like an SGS term (Boris, Oran), and you can have LES without modeling the SGS terms at all. Recently Morinishi proposed a modification of a mixed two-parameter dynamic SGS model, which takes into account the influence of the numerical dissipation of the scheme. Cool isn't it?! But, earlier studies have shown that, when the sub-grid scale cut-off is in the inertial sub-range, the SGS term parametrized by the Smagorinsky model is of the order delta ^ (2/3)! This may be the secret why second order scheme still works well for LES. I think that both the convective and diffusive terms have to be discretized with higher order accuracy if you want to obtain better results, or the same results on coarser grids. I will definitely look for higher order compact schemes in the future (after my disertation). For complex geometries… This is possible while using Residual Distribution schemes!

(2) For the case with complex (or even simple) geometries, do people use adaptive griding with LES? If not, why?

Adaptive griding can be successful in capturing the small, but energy containing scales of the turbulence, as for instance close to the wall, while having a much coarser grid in regions where this scales are bigger or there is no turbulence at all. Usually people consider that the first filter (or the SGS cut-off) is of dimension grid size, while the second one (test filter) which is used when a dynamic procedure for computing the model parameter(s) is employed, is two times bigger. Jumps in the grid size will normally lead to a jump in the filter width. BUT, there is a problem that comes from the variable width filters: usually they do not commute with the differentiation operator. A special class of such filters, for which the commutation error can be expressed directly and included in the computation, has been invented. I don't know if it is successful because I haven't seen it to often. People complain that they can see the grid in the solution, when the jump in the grid size happens. (Which is not so rare also when homogeneously refined grids are used, no?, if the grid has jumps in size).

Please consider that these answers are coming from a non-specialist in LES!

Best regards, Doru