I am a research scholars from IIT Madras.I have currently started understanding an LES code.I have a hand full of doubts.One of them is that i understood how to apply the filters to the NS equations and deriving the tou terms from it .But I do not understand how to apply these filters numerically.ie.,how to find u bar and u bar capped values.Please can any one help me out of these.

Quite a bit of work on discrete filters has been done. Why don't you make a trip to the library? Look at CTR research briefs, there a number of papers on this topic by T.S. Lund.

Dear Mr.Mohit

Hope ur a student.Can u give some more information on this.

The Navier-Stokes equations represent a continuum. The LES equations are obtained by filtering them. As such, the filtering operation preceeds the discretization (FVM, FEM, spectral scheme etc.) and is purely a mathematical operation. Well, that's theory.

In practice, when the Navier-Stokes equations are discretized on a spatial grid, it is assumed that the equations obtained are not for the actual continuous variables (like the continuous velocity fields) but rather their filtered counterparts. So the so called "grid" filter is an implicit filter that depends on the type of discretization scheme (FEM, FDM, spectral etc.) and the specific approximation (second order central scheme, compact scheme, upwind scheme etc.). The filtered equations are supplemented with models for subgrid stresses due to the fact that turbulence fields have a broad spectra (multiscale spatial and temporal flucuations) that cannot be captured on a typical LES grid.

The test filters are discrete filters, are well defined and can easily be applied to variables on the LES grid.

While the test filter is user defined, grid filter is not. It depends on the grid, discretization scheme, type of flow. I can suggest a exercise to obtain the form the grid filter from LES generated data and DNS data if you are interested.

Dear Kalyan

I think i should first be clear about Implicit filter and discrete filter can you guide me some more on this topic.And you said some excercise you are always welcome for such excercisses . I am always ready.

yours sicerely Senthil ks_kum@usa.net sen@aero.iitm.ernet.in

Discrete filters are relative simple.

Eg : {u(i)}=0.25*u(i-1) + 0.5*u(i) + 0.25*u(i-1) where "i" denotes a spatial location and u(i) is any field (velocity, pressure etc.) whose values are known at discrete locations on a grid.

The test filters used in most dynamic models (Germano et al.) are discrete filters that act on LES generated fields.

The finite volume (FV) formulation is perhaps one of the easiest ways to understand the implicit filtering concept. In cell-centered FV schemes (i.e., schemes that use grids that have dependent variables such as velocities, density etc. defined at the center of the cells), the velocity variable at the center of a cell does not represent the value of velocity at that point, rather it represents the average value of velocity in that cell. If the cells are rectangular, then the spatial average of any quantity in that cell is nothing but a "box-filtered" quantity. The width of the box filter is the same as that of the cell.

i.e. Box filter = spatial average

If you have a LES code, you can always find implicit filter in it through a simple exercise provided you also have the resources to conduct a direct simulation (DNS).

Let FT(q) denote Fourier Transform of q. Then, Let G and <q> denote the LES filter and the filtered value of q. Then,

FT({q}) = FT(q) FT(G)

An LES code would give you {q}. If remove the LES model (subgrid stress model) out of your code and run it on a grid that can resolve the approximate Kolmogorov length scale in a given turbulent flow, your can conduct a direct simulation. The direct simulation would give you q (unfiltered q). From the above equation, you can now get the Fourier transform of G given q and {q}.

Transform FT(G) using an inverse FT to get the filter function. This is your implicit filter. However, if you conduct this exercise using two different turbulent flows (e.g. isotropic turbulence and a turbulent mixing layer), then you are likely to end up with different filter functions. So keep in mind that the implicit filter also depends on the type of turbulence if not as much on the scheme and the LES model used.

Dear people From kalyan i come to know how to apply test filter.But any can explain me how to and which direction should i apply the test filter in the case of flow over a sqr cylinder abn why. thanks in advance senthil k .