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December 10, 2002, 22:17 
the commute error in LES

#1 
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the commute error is zore with the uniform mesh.is this means i did not think about the commute error in computational reference frame? i know the concept of the homogeneous and the isotropic turbulence,but i'm too fool to apply it in practice.could you help me,and show some dome in common.
thank everyone for your help 

December 11, 2002, 17:09 
Re: the commute error in LES

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ref: S. Jordan (J. Comp. Phys.)....it explains filtering in computational domain to take care of commutation errors....
Just by changing from physical to computational domain, you can't get rid of these errors...need more than that!! take care Mayank 

December 16, 2002, 12:39 
Re: the commute error in LES

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Hi there,
Like suggested by Mayank, you can check out papers by Jordan, but it is a little hard to read!! For in depth and clear analysis associated with commutation error, take a look at the following papers: [1] Vasilyev, Lund and Moin, Journal of Comp. Phys., vol 146, pp 82104, 1998. [2] Ghosal and Moin, journal of Comp. Phys., vol 118, pp 2437, 1995 I hope this helps. Sincerely, Frederic Felten. 

December 16, 2002, 15:57 
Re: the commute error in LES

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Hi,
Ghosal and Moin, journal of Comp. Phys., vol 118, pp 2437, 1995 : Basic equations for LES are derived for nonuniform grids (You won't believe that the problem of commutation error is noticed as early as mid 70s(..and addressed without much success), I guess in Moin's work..perhaps during his disseration)...took another 20 years to get to this seminal paper!!!...however, the perturbative strategy to address this issue is BAD... Vasilyev, Lund and Moin, Journal of Comp. Phys., vol 146, pp 82104, 1998 : Another classic (or soon to be) paper that addressed the issue of getting rid of these errors by constructing filters that satisfy the vanishing moments criterion...very elegant theory, but the problem is the vanishing moment requirement is in contrast with the realizability requirement (which means positivity of filter kernel...ref: Vreman, Geurts, Keurten in JFM) Truly speaking this issue is not yet satisfactorily resolved...However, there are alternative formulations for LES that can either completely avoid this issue or partially address it (Check for Adrain's optimal LES formulation (TAM report), Pope's projection onto local basis function formulation (lecture notes in physics), Hughes's multiscale formulation (umm..I guess computational mechanics)..and some more) ..Again Cook's paper (J. comp phy.)on adaptive refinement with consistency constraint on filters gives an idea for applying filtering on AMR type cartesian meshes. Hope this helps Mayank 

December 16, 2002, 22:48 
Re: the commute error in LES

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Dear Mayank and Frederic
You are so warmhearted that I appreciate your help. I have read some papers about error analysis,and I known the error maybe reach the O(delta**2),where delta is the mesh skip.If I use the macomark scheme(only second order resolution),the commute error is the same order as truncate error.In practice need I think about the commute error? thanks for your help. sincerely. Tom 

December 18, 2002, 10:42 
Re: the commute error in LES

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hi mayank,
would you qualify the BAD in your post? i haven't followed LES literature in a while now and i am curious. is jordan's work mentioned before more consistent then? regards, chidu... 

December 21, 2002, 05:03 
Re: the commute error in LES

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Hi Chidu, There was a paper by DesJardin (may be couple of years back)...primary result being that the perturbative strategy for taking care of Commutation errors is an illposed and illconditioned problem...it was very difficult to get a numerical solution for these set of equations...and that's BAD.
what are you currently working on? (If I'm not mistaken, you did your masters from Iowa with Pletcher's group and then moved to Switzerland for Ph.D...I met another guy Ravikanth at 3rd AFOSR conf. on DNS/LES..If I recall correctly, he did mention about "you"..that was in 2001..may be I'm wrong...also, I had the oppurtunity to listen to Fredric's talk there..nice job!!) Jordan's work is "interesting"...He solves for filtered fields in computational domain...therefore filter commutes with differenciation operation here..it is equivalent to filtering along the curved grid lines in physical domain...however, it is apparent that it doesnot remove the error we're talking to begin with (think about it!! )...he makes assumptions about zero Dirichelet B.C. or periodic B.C. for this error to go to zero when integrated over the entire computational domain (again, that is not how we started quantifying this error...analogy being..integral balance of mass flux in computational domain does not imply that divergence of the field is zero at all point...for every CV based scheme can do integral balance..yet divergence is at best second order accurate) As I mentioned earlier, treating LES equations in the realms of convolution filtering, we haven't found a satisfactory solution for commutation errors yet...alternate formulations exist where one can eliminate these issues (see previous post)...needs to be demonstrated on numerous validation cases cheers Mayank 

December 21, 2002, 05:17 
Re: the commute error in LES

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Hi Tom, refer to Layton's work on error analysis of commutation errors...you'll be surprised with some of the results...for one being...they recommend solving LES equations in weak form using variational principles..only then you can get rid of commutation errors...Strong form can give rise to errors of O(1)!!
Commutation errors arise from two sources, filterwidth variability and the crossingover of filter support near the domain boundary (refer to Fureby et al in theoretical and comp. fluid dynamics (TCFD)...very nice paper)....therefore domain boundaries will be a challenge... In practice, you should have highorder schemes for LES...second was fine, when resources were scarce...A "True" LES is yet to be performed. If you have highorder scheme, you should eliminate all possible sources of loworder errors, commutation error being one of them. hope this post provides some clarity Mayank 

December 21, 2002, 10:56 
Re: the commute error in LES

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Hi Mayank,
Yeah, I am a friend of Ravikanth. I am working on particleladen turbulent flows. What are you doing? Looks like you are in the thick of things in LES. I started reading the paper by Jordan and then gave up. Didn't have the patience to dig in. Can you give the reference of DesJardin? regards, Chidu... 

December 22, 2002, 08:55 
Re: the commute error in LES

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Hi Chidu,
I'm primarily working on LES of gasturbine cooling flows: filmcooling as well as internal cooling. I'm also working on biological flows using immersed boundary method. Most of the work done so far is very elementary, but I hope to go deeper into this area. current problems of interest (i.e. funded) are suspension feeding by bivalves and development of glaucoma in human eye. I thought that Jordan's paper was relatively easier to read than other LES papers...anyway, you can read it some other time, whenever you are FREE!!!(like that ever happens) DesJardin's paper...I've to dig it up (I know I've it!!). It was a conference paper...that makes it even more difficult to find. bye Mayank 

December 23, 2002, 13:15 
Re: the commute error in LES

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I agree with most of what Mayank has pointed out. However, I am not sure if pursuit of a "true LES" (as Mayank puts it) is even worthwhile. After all most errors that we are talking about here have to do with discretization of a continuous systems. There is always going to be the issue of closure (I don't mean LES closure).
As many in turbulence community may already know, continuous and discrete systems are topologically very different dynamical systems. Even in a highly refined DNS, only the lower order statistics are predicted well. That's why we see very different kurtosis being reported from spatial and spectral simulations. If there is an obvious way of eliminating the much discussed commutation errors, that is fine. But, most tricks that I have come across (although I follow LES literature less closely than I used to couple of years ago) can not be extended to the real turbulence/mixing problems of interest. Most of the applications of LES is in internal flows that involve sprays, combustion (density variations) and significant complex geometries that do not accomodate cartesian meshes. The idea that you start with incompressible flow in simple geometries and work upto the complex problems has been the promise many LES researchers have been making for about 10 years now but the reality is far from it. This is partly due to everyone operating in their ivory towers. People who work on incompressible turbulence in simple geometries are reluctant to move to more complex flows. Their expectation is that they solve some fundamental conceptual problems in these simple flows and some one else should build on their work by extending it to more complex flows that involve processes like sprays, combustion etc. I am not particularly blaming anyone. After all, in the present day, most researchers seldom have long term funding to see their ideas implemented fully. Perhaps collaboration is the only way LES is going to move uotp the next level. 

December 25, 2002, 05:09 
Re: the commute error in LES

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Hi Kalyan, Really nice to hear from you...(last time I actively participated in discussion with you was on McDonnough's SGS schemes using logistic maps (or dynamical systems)...is that right?)
By "true" I meant a methodology that respects the known physical and mathematical constraints for a generic system...be it continuous or discrete...usually we accept only those discrete systems that can mimic the "original" continuous system to begin with. I share the similar disappointment when people propose a methodology on very simple system (can be at best academic)...and leave the headaches of complex systems unaddressed. I can only hope that some day these research activities will converge towards the "true" objective (this time "true" being the actual problem at hand!!)...this however requires a program that stresses on both the fundamental as well as applied aspects of the problem (which is very rare). You pointed out collaboration as the only way to move to next level...and that's rare too!! 

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