I have problem with dynamic filtering procedure in LES. I know the filtering in wave space with spectral cut off filter, But How can I filter it in actual physical space? Especially in non-uniform cartesian coordinates.

Thank you.

Hi Takuya,

There are several filters like tophat or gaussian etc. which can be used in physical space. The question you have asked is of fundamental concern. The filtering operation on non-uniform grid does not commute with the differentiation operation, thus leading to "commutation errors" (if you are using a grid based filter whose filter width becomes function of space variables on non-uniform grids. ref: ghosal et al (1995) J. Comp. Phys.). If one does not mind second order errors i.e. commutation errors... one can write on nonuniform stencil, the physical space filter too. Obviously, that's not the solution to your problem. If one wants to reduce commutation error, there is a procedure given in Vasilyev et al (1997) (CTR annual research briefs). Again, those filters violate the "realizability requirement". Most of the researchers in LES are just ignoring "commutation errors" and pushing for high order accuracy schemes (take it with a pinch of salt!!!). Status of filtering on non-uniform grids is still in infancy stage. I'm not aware of any consistent way of grid based filtering in physical space which is realizable as well as free of commutation errors. I have more references regarding this issue, in case you are interested.

regards Mayank Tyagi