Implementation of Germano-Lilly model in LES
I am currently attempting to implement the Germano-Lilly subgrid model into a LES code, but I am having some difficulties. The code will be used for studying boundary layers and free shear layers.
Initially, I have set the code to calculate Lij, and this is done by test-filtering the veolcity components (and the products), in the manner of the reference the reference (http://www.tfd.chalmers.se/doct/comp..._files/les.pdf). Now, the values of Lij behave as expected - tending to zero near the wall and constant in the free-stream.
My code then calculates the test filtered Sij term (S^ij), and this is where my problems begin. I am unclear as to the whether the dx in the equation S^ij = 1/2 (du^i/dxj + du^j/dxi) corresponds to the test-filter width or to that of the grid spacing.
Also, after I have test-filtered the |S|Sij term, I find that I need to set a boundary conditions for this term to close the system on my computational domain. Is there a simple way to do this, or have I made a bad assumption in how my test-filtering works?
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