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Old   June 7, 2003, 00:01
Default Question about QUICK at boundaries
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I'm looking in page 128 of "An Introduction to Computational Fluid Dynamics" by Versteeg and Malalasekra copyrighted in 1995. In the example problem (1-D, convection-diffusion) illustrating QUICK, I have a problem deriving the far RHS term of Eqn. 5.54.

More specifically, how do I go from one form of the DIFFUSIVE FLUX THROUGH THE WEST BOUNDARY, D_A (#_P - #_A), to the following form {D_A [ 9(#_P) 8(#_A) - #_E ] } / 3 .

where D_A = diffusion coefficient at west boundary; _A = at west boundary; _P = at central node; _E = at east node; _0 = at mirror node; # = transported property;

If anybody could answer this before I go to the paper by Leonard (1979), that would be greatly appreciated. I already understand how the mirror node works and how the value of the transported property at the mirror node is: #_0 = 2(#_A) - #_P .

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Old   June 7, 2003, 12:15
Default Re: Question about QUICK at boundaries
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If I understand your question, this has nothing to do with QUICK, which is for the convective terms. The simple form of the diffusive flux at the boundary produces a zeroth order truncation error for the diffusion term div(D grad #), but the second and more complicated form is first order. You can verify this by the usual Taylor series expansion of the difference equations. Your expression for #_0 leads to the inaccurate form of the diffusion term. The expression for #_0 corresponding to the first order diffusion term has a term proportional to #_E. The algebra is straightforward.
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Old   June 7, 2003, 12:36
Default Re: Question about QUICK at boundaries
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Thanks, that's the answer I was looking for. And yes, I had a brain freeze, I should not have even mentioned QUICK which as you mentioned relates to convective terms.
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