CFD lecture 11

# CFD lecture 11 - Computational Fluid Dynamics Lecture 11...

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Computational Fluid Dynamics Lecture 11 Finite Elements: 1 () j x φ 0 j-2 j-1 j j+1 j+2 0 x 2 x 0 x 2 x upslope on interval 0 . downslope on interval 0 . x xx x x x x =< < ∆− < 1 jj + 0 x Region where both are non zero. 23 2 11 22 00 0 2 2 3 2 0 , 2 3 6 , 6 1 , 3 j j S x j j S x x x x x x Id x d x x x x d x x x x x x x x d x x φφ ∆∆ ++ −−    == = = = =    = =+ = ∫∫ 2 2 0 12 23 3 33 x x 2 x x x x x x x + + = +∆−∆+ = We are seeking the expansion of 1

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0 C tx ψ ∂∂ += With the Galerkin approximation 11 0 NN nn nk n k S a IC a d x φ == ∑∑ Using: () 0 22 2 0 00 2 1 0 x jj SS xx x j j dx dx dx xx x x dx dx dx x x x x x x φφ −+ ∆∆ ∆−  −= = =  ∂∂ ∆   =+ =− +  ∂∆ ∆ ∆  ∫∫∫ ∫∫ ∫ x = Since all other integrals involving products of the expansion functions, or their derivatives are zero.
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CFD lecture 11 - Computational Fluid Dynamics Lecture 11...

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