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July 28, 2004, 16:58 
LES (explicit) filtering

#1 
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Dear friends,
Is it possible to do (explicit) filtering for nondynamic SGS models like Smagorinsky or 1 equation models? and if so, does it siginificantly improve the results or one should use explicit filtering only in dynamnic models? How expensive computationally is explicit filtering? (typically) Any idea would be helpful, Thanks. 

July 29, 2004, 12:13 
Re: LES (explicit) filtering

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In nondynamic SGS models, one assumes that the Cs value does not change and hence there is no need for explicit filtering.
In dynamic models, if one wants to do grid resolution studies, then the need for explicit filtering is warranted. Have a look at this paper http://ctr.stanford.edu/ResBriefs02/gullbrand.pdf 

July 29, 2004, 18:03 
Re: LES (explicit) filtering

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Hi,
Indeed you can perform explicit (or pre) filtering even if the SGS model is nondynamic. Although Cs remains constant, the lengthscale delta can be adjusted. So the basic idea is to replace a value of delta_mesh based on the size of the grid (Shannon theorem on sampled data) with a value of delta_filter based on the cutoff length of the explicit filter. There are some advantages in doing so. First this is the only way to ensure a true gridindependent solution in the LES framework by reducing the cell size while keeping the filter size constant. It also allows to suppress the smallest "resolved scale" that are the most contaminated by the numerical errors of the numerical scheme. You also have a better control of the filtering process that can be used to fit the requirement of the SGS model (I think there were papers by Piomelli, among others, dedicated to that subject). But there are also drawbacks: you have to spend some CPU time to perform the explicit filtering. Moreover, you reduce the number of physical degree of freedom ("number" of turbulent scales in your solution) while keeping constant the numerical degrees of freedom (number of grid points). Eventually, such a computation rely more on the subgrid model. So basically you have to choose between not to accurately resolve the smallest scales or to model them. What do you trust most: the numerical scheme or the subgrid model? I agree that such an "answer" is not really helpful. The following one could be. If two computations are carried out with the same delta, one arising from an explicit filtering and the other arising from the implicit mesh size filtering, the former seems to lead to (slightly) better results (Gullbrand and Chow; Meyer, Geurts and Baelmans). However it will be at the expense of the CPU time, because in such a computation the implicit delta_mesh has to be really smaller than the explicit delta_filter so as to take full advantage of the explicit filter effects. Say for instance that delta_mesh=delta_filter/2 (for gridindependency, a ratio from 6 to 8 could be necessary, see Geurts and Frohlich). Then to obtain the same amount of physical information (regardless of their quality), the computation will cost at least 2^4 time more than the unfiltered one (twice the number of cells in every space directions and a timestep roughly divided by 2 due to CFL considerations). And I'm far from being convinced that such a computation would beat a nonfiltered one of a similar CPU cost. That's probably why almost all LES are implicitly filtered, with the few exceptions of some theoretical works. Some references: book by Sagaut (see book section), chapter 7 in the first edition; The previously mentionned paper by Gullbrand or its JFM extension (Gullbrand and Chow , JFM 495, pp. 323341, 2003) Papers by Geurts and Frohlich (Phys. Fluids 14(6), pp. L41L44, 2002) and by Meyer, Geurts and Baelmans (Phys. Fluids 5(9), pp. 27402755, 2003). Hope this helps. 

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