l9 - Lecture 9: A First Look at the Diffusion Equation...

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Lecture 9: A First Look at the Diffusion Equation (cont’d)
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Last Time… We looked at Conjugate heat transfer » Spatially variable , particularly when there are material discontinuities Source linearization Under-relaxation
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This Time… Will look at Linear solvers, particularly TDMA Start looking at unsteady conduction
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Linear Solvers Let’s re-visit linear solvers for 2D structured meshes Consider 1D discrete equation for point P
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Linear Solvers Recast using slightly different notation One equation like this for each grid point i=1,2,3, …, N For i=1, c 1 =0. Also b N =0 i i i i i i i d c b a 1 1
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Tri-Diagonal Matrix Algorithm (TDMA) For ith grid point: For boundary points: c 1 =0; b N =0 Using equation for point 1 write 1 = f( 2 ). Substitute into equation for 2 to eliminate 1 and write 2 = f( 3 ) Repeat procedure until Nth equation is reached; find N Back substitute to find
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This note was uploaded on 12/29/2011 for the course ME 608 taught by Professor Na during the Fall '10 term at Purdue University-West Lafayette.

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l9 - Lecture 9: A First Look at the Diffusion Equation...

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