Dynamic SGS model procedure in Large eddy simulation
Dear guys
i'm working on kiva3v and make smagorinsky and kdelta oneeq SGS models. the standard forms have been done and now i'm going to make sgs eddy viscosity in the dynamic form for both models. i have one question. as you know dynamic procedure needs at least one level explicit filter which i use top hat for nodes. first i have all nodes velocity fields and i choose one direction to use a filter (actually it is not true but lets think just x direction in xyz system). i make a averaged value of all quantity i need to use in dynamic eq and use top hat three grid for three side by side cells in the x direction. you know kiva choose node by ifirst to ncells and it can call the front and back nodes by some commands so i use this procedure in kiva to make my dynamic form. my question is this, is it a true way to make a dynamic filtering procedure? should i make filtering in all three direction and choose the averaged value? i just read some papers that recommend to use dynamic filtering in streamline. what do you suggest me? 
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In principle, the type of test filtering for the dynamic procedure has not to be equal to the main one. That means you can use a 2D test filtering, this happens commonly for plane channel flow. Note that for Cartesian grids, three subsequent 1D filter along x,y and z corresponds to a 3D filter over a volume. A more specific answer depends on the problem you are solving. 
Thank you.
I think in some way i get your meaning. but let me give some more explanation to get more to my problem http://http.developer.nvidia.com/GPU...ks/22fig03.jpg just consider one cells plane, then consider one row of that plane, is it true to act dynamic procedure by three side cells (top hat) and after finishing the row, just change and go to next row and go on,till finish the plane and go to next plane and go on...? (sth like we do in TDMA algorithm for 3d grid)? 
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2) what about your testtogrid filter ratio, you wanto to fix the value =2? 
1)i dont get your meaning by 2d or 3d test filter. what i have done, is sth like i explaned about the picture above in 3d mesh grid. i want to know if it is right or wrong and for your explanation about 2d or 3d test filter, i think it should be sth 1d test filter!
2) about my testtogrid ration, i use grid filter as single cell volume^(0.33) and use three side by side cells volumes^(0.33) as test filter length. so in different position it gives me different testtogrid ration between almost 1.2 to 2.7, again is this procedure true? 
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1) the type of test filtering depends also on the flow problem, if your problem is a plane channel flow,e.g. homogeneous in the x and z directions (streamwise and spanwise), you can do a 2d filter, (an area average) in x,z for example using a 3x3 stencil. If you are solving homogeneous isotropic turbulence, a 3d test filtering (that is a volume average) should be considered, for example over a 3x3x3 stencil. 2) the testtogrid ratio is an input parameter in the dynamic procedure, do you think to use a variable value depending on the local position? That implies some difference in the procedure 
my grid is a engine cylinder with intakeexhaust port and combustion chamber geometry, which dose not allow me to use a uniform mesh. so i think i have to use a dynamic procedure with testtogrid ratio by position and can't to use a constant ratio. consider a cylinder with a axis in z direction. i use a plane to do my dynamic procedure. for example between z=10mm and z=11 mm, all cells cubic cells between these planes are considered. i averaged of all node value firstly to make a averaged value for 8 nodes of each cells, then use three side by side cells and make a top hat 3node filter. use this procedure for all cells of the plane then shift to other plane and use the same procedure.

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you have also a piston moving in it? I think you have to build, for each computational node, a local volume surrounding it in such a way that a 3D volume average can be computed. If you are using a structured grid a 3x3x3 local grid stencil can be used. The numerical implementation can be done following your idea, fix a z=constant plane compute and store the area average values and repeat for each z plane. Then, compute the 1D average along z by using the 2D averaged field. But if you are using an unstructured grid the number of volumes depends on the topology and the procedure can be more complex. The final filtered field can be used in the dynamic procedure. However, the filtertogrid ratio value must be also evaluated correctly. 
please consider this image
http://i43.tinypic.com/2cqo1nq.jpg for each cell, i have 4 node. so i compute the averaged value of velocity component (u,v,w) for each cell by its 8 nodes. then consider cell1,2 and 3 in row 1 @ z=cte, i use top hat test filter by these three cell, in the direction of row 1 axis, then i use this method to finish all cells in row 1 and go to next row (row2 and ...) after finishing all the row of z=cte, i goto next plane in another z position how does that procedure sound? 
I have to distinguish between the test filtering procedure and its numerical implementation ...
If you want to use a tophat filter, in a 2d plane say (x,y), you have to chose its width. Therefore, you write the continuous expression: f_test(x,y) = (1/Deltax/Deltay) * Int [yDeltay/2,y+Deltay/2] dy' Int[xDeltax/2,x+Deltax/2] f(x',y') dx' For example, you can choose Deltax=2*Dx and Deltay=2*Dy. Now you have to numerically compute the above integrals by using a proper discretization. For example, you can use a 2D Simpson rule. Therefore, centred at i,j you need of a stencil of 9 nodes going from i1,j1 up to i+1,j+1. The weights of the integration formula can be found in many textbooks. You can do that for any i,j nodes in the x,y plane. Then repeat for all the z planes. Finally, if you want to make the test filter threedimensional, you have to average again the 2d filtered field using the 1d formula for the z direction. 
Professor Denaro;
Could you please provide me with technical information, papers or book about the 3x3 stencil or 3x3x3 stenticl you mentioned for 2D and 3D explicit filtering respectively? I am trying to upgrade the LES code I have from Standard Smagorinsky to the dynamic procedure. However, I am very confused. Also, you mentioned that for channelf flows (my case) an area average is enough (over the homogeneous directions). Nonetheless, the test filter is applied over the Strain Tensor and Strain norm wich are tensors. Thus, I cannot visualize the procedure clearly. Definitely, because the explicit procedure for the test filtering is not clear enough. I read your paper: What does Finite Volume  Based implicit filtering really resolve in LES and in the section 4.1 describes the discretization of the testfilter. However, it is not clear (at least for me) the expression you came up with. Very respectfully Julio 
Hello Julio,
be careful, the testfiltering is applied on the main filtered velocity field, not on the stress tensor (derivative could not commute with filtering)... the test filtering can be practically implemented as a simple discretization of the integral over a wider stencil, is a numerical issue. You can find some further details here: https://www.researchgate.net/publica...gorinsky_model https://www.researchgate.net/publica...gorinsky_model 
Thank you very much professor for sharing this paper with me. I am reading the paper and I hope to answer the questions regarding the test filtering. Also, thank you for clarifying that the test filter acts on the velocity field and it will yield to the filtered strain tensor.
Respectfully Julio Mendez 
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Dear Professor; I read the paper already, as well as other references from the same paper. Although it helped me a lot (now I understand why you said that the filtering is a numerical issue) I still have few questions.
Equation (15) from page 37; you wrote the expression for a 2D local average (box filter) which will be applied over the homogeneous directions. The computational stencil of 2*deltax*2*deltay. I am assuming that delta is the grid size and the test filter is 2*delta. You mentioned the you used the fourth order Simpson rule. However, I was not able to derive the expression and obtain the same factor (1/36, 16 and 4 ) from your papers. Are these values unique for your gird size, and therefore for the width of the test filter?. What paper or textbook do you recommend me to read to obtain my own coefficients? in case those coefficients are not universial for the Box (tophat) and for a thest filter with a width 2 times greater than the grid size (delta) Thanks Julio Mendez 
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the formula is generally valid for uniform meshes, you can find the same formula at page 75 of the book of Ferziger & Peric 

Thank you very much professor for your kindness.
What is surprising for me, is that the filter is a volume average (tophat). Finally, I am thinking about the influence of the test filter width. Does it only influence the location at which V_(i+1,j,k) and so forth are evaluated, while the expression remain unchanged? I mean, if the test filter is 2*delta, the V_(i+1,j,k) is the very next volume, whereas if the test filter is 3*delta is the second volume next to V(i,j,k) ? 
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Sorry, I am not sure about your question ..If you would define the filter width equal to 3*delta then just define the integral over [x3/2*delta, x+3/2*delta] and use a proper discretization involving a wider stencil. This can be done for all i,j,k nodes over overlapping areas 
Thank you very much professor; I am still struggling with this but I expect to fully understand with the material you gave me.
Professor, I read the other paper (Direct and LargeEddy Simulation VIII Volume 15 of the series ERCOFTAC Series pp 2732). There, you used two different test width: 3*deltaX*3*deltaZ and 5*deltaX*3deltaZ. Also, in the section 5.1 from: A new development of the dynamic procedure in largeeddy simulation based on a Finite Volume integral approach. Application to stratified turbulence you specified a stencil of 3x3 for alpha = 2 and 5x5 for alpha = 4. Having said that: the width of the test filter what basically means is the amount of volumes I use to do the filtering or (volume average) rather than antoher mesh with different delta that overlap the main mesh?. On the other hand, the velocity field is the one I apply the test filter on. Hence, I have to interpolate the velocity from the cell (staggered grid) to the center of the node to have these velocity ready for the filtering procedure? Finally, professor do you have the expression (as you presented for 2*deltaX*2deltaY in On the relevance of the type of contraction of the Germano identity in the new integralbased dynamic Smagorinsky model) for the other test width you presented on the other two works I referred above? Thanks in advances Very Respectfully Julio Mendez 
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