DYNAMIC FILTERING

Paul

the dynamic smagorinsky model in LES solves the equation:

Lij(a) = //test_filtered//(C*bij) - (C*aij)

where [a = aniostropic component of known Leonard stress] [bij = the grid filtered subgrid stress] [aij = the test filtered subgrid stress] [C = required dynamic smagorinsky constant]

(aij and bij are both symmetric and traceless tensors)

it is said that this represents a system of FIVE independent equations. Can someone please let me know what these 5 equations are as i would have thought there was either 3 or 6 equations?

i.e. where [Mij = //test_filtered//(bij) - (aij)]

1) L12 = C*M12, 2) L13 = C*M13, 3) L23 = C*M23, 4) L12 = L21, 5) L13 = L31, 6) L23 = L32