CFD lecture 23 - Computational Fluid Dynamics Lecture 23...

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Computational Fluid Dynamics Lecture 23 Wrap up on LES Notes say (Ferziger). 2 2 1 2 2 2 but I said how do these compare? j i i j i j v C s v C u u u v x x x τ τ ε ε = = = + eqn. 1-1-8 Hinze, pg 71, term IV. What does j i j i u u x x + look like? For i 1,3; 1,3 j = = there are 9 terms: This is all one equation; so i , j indices do not separate into 3 equations like in momentum equations. j i j i u v w u u u u v w v v v u v u x x x x y z y y y x y z z z u w w w w x x z x y z + + + + + + + + + + + + + + = + + + + Which has two occurrences of each term. You could use continuity and throw out groups of 2 2 1 Now 2 j i j i j i ij j i u v w x y z u u v w u u v w x x x x y z z u u S x x + + + = + + + + + = + y pg. 381 Lesieur; eqn. 2.3 and 4.3 Ferziger; pg 252 Peyret & Taylor 1
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and obviously ( ) 1 2 2 1 2 Finally
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