2 LES questions
First of all, I should precise that I work with OpenFoam, trying to make LES simualtions for wind engineering. So my questions concern only implicit filtering.
My first question concerns the grid. I have read in different places that the filter operator has to be commutative with differential operators (the order of application of these operators does not matter). And I understood that this is not the case with non-uniform grids. By the way, a lot of people is working with LES on non-uniform grids. Does anyone can explain me?
In my opinion, it is true that LES grids have to be uniform. Let's imagine a non uniform grid, cartesian, with a x2 refinement (the face of one cell divides in 4 little faces of 4 little cells). What happens to eddies modelled in the large cell and calculated in the small cell ? In the first one, the filter beeing twice larger than in the second, how can these intermediate eddies communicate between the large and small cells ?
My second question is a bit more linked with OpenFoam, but I think it is not specific and can be discussed here. I am using a LES turbulence model called oneEqEddy , which is a model with one transport equation for k. But here, I don't understand the meaning of k. Usually, it represents the local turbulent kinetic energy density, defined as the stantard deviation of the velocity. Something like k=<u'²> , where < . > is the temporal average.
On the other hand, the LES filtering is a spatial filter, and we have a value for each time step.
Thus, what does k represent in this oneEqEddy model ? Is it the spatial variations of u'² in a given cell ?
If I want to reconstruct the full spectra Turbulence Intensity at one point. I can calculate explicitely the time variations resolved by the LES. Should I had k ? But at which time step? The mean (averages in time) value of k ? In this case, what about the explicit variations of k ? Aren't they also a kind of fluctuations so to be added to the Turbulence?
As you see, I think my understanding of what is k is a bit short...
1) To give an answer, let me start from the beginning using the simple Burgers equation as example:
du/dt + Div ( u^2/2) = 0
Now if you apply the filtering you actually have [Div ( u^2/2)]_bar. This term is the key-point, it is very common in the LES community to commute filtering and divergence operator and working on Div [( u^2/2)]_bar .
But there is no mathematical or physical requirement to do that ... is only a way to continue working on a differential form for the filtered equation without using explicit filtering.
As you said, the commutation requires some mathematical property that for non-uniform filter does not hold. Ghosal showed that the additional commutation term are of second order of magnitude in the filter width. That means that if you use a second order discretization you can argue that such additional terms can be disregarded. Otherwise, special filtering that commutes (at least to the extent of some order...) were proposed by Vasyliev et al.
To tell the true, I prefere working on the term [Div ( u^2/2)]_bar.
Furthermore, the variable filter width does not effect comunication between a filtered value and the adjacent one... you have filtered equations that are related to different filter width.
2) I don't know details of the OF implemented model you cited, furthermore I never used SGS model based on kinetic energy ... I suggest to check the dynamic modelling at first..
unfortunately, OF is very poorly documented ...
what is usually intended for k in LES of incompressible flows is half the trace of the SGS stress tensor. So, in theory, it is actually far from the temporal average value.
Now, there are several models based on an equation for k (more probably, those usually implemented in unstructured codes are mostly based on the version of Kim and Menon or the one of Davidson), but for all of them this quantity is actually to be intended a la URANS.
What i mean here is that yes, in theory, the k value (and the full modeled SGS tensor) should be used in determining the RMS fluctuations but they have the same significance of a Reynolds stress tensor reconstructed from the eddy viscosity and the Boussinesq Hypothesis in URANS.
I don't know how much space there is here for interpretation, but i would never use such models in reconstructing the statistics, as their role in the simulation is clearly different and i would not mix the two things.
In contrast, structural SGS models are well suited for this as this is their role also in the simulation.
Of course, you can use the one equation model in the computations and then resort to a different technique to compute the SGS contribution to the fluctuations (say, a scale similar one)
However, you can find a nice discussion on this in the book of Sagaut (Chap. 9 if i remember well).
LES for pimpleFOAM
sorry for asking this question in this thread ,
I have small doubt regarding using LES turbulence model for pimpleFOAM
I wanted to know what kind of BC variable should present there in zero directory for pimpleFOAM LES combination for incompressible flow.
e.g. for running simpleFOAM for incompressible flow one can have
p,U,nuT, k, omega/epsilon these parameters .
Like that what are the BC variables required for LES turbulence model for pimpleFOAM solver .
First, you need U and p.
Then, it depends on the LES model you are using. I am using oneEqEddy, which needs k and also (I don't understand why) nuSgs. If you are using classic Smagorinsky, you need only nuSgs.
'hope this can help you...
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