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Handling of diffusion flux terms at the boundaries with QUICK scheme |
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January 18, 2020, 04:19 |
Handling of diffusion flux terms at the boundaries with QUICK scheme
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#1 |
New Member
Farhad Hasanli
Join Date: Jan 2020
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Hello everyone,
It's my first time posting here, so I am sorry if I am not posting in the proper forum or for any other mistakes I may have made. So, my question is about the theory of the QUICK scheme. While reading Versteeg and Malalasekera's book "An Introduction to Computational Fluid Dynamics: The Finite Volume Method", I have encountered a problem with the handling of the diffusion boundary terms. The explanation for the equation seems a bit vague. I have attached two pictures. It seems like eq. 5.54 for diffusion flux at the boundaries emerged out of nowhere. I have tried to find online about this issue, but with no success. I would appreciate it if someone could explain the reasoning behind that formula. Thank you in advance |
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January 18, 2020, 06:18 |
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#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,849
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Quote:
Not sure about but it seems a derivative computed from a quadratic interpolation on 3 nodes at different step sizes, that is A and P at h/2 and P and E at h. You could check that |
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January 18, 2020, 07:11 |
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#3 |
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Filippo Maria Denaro
Join Date: Jul 2010
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January 20, 2020, 06:19 |
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#4 | |
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Farhad Hasanli
Join Date: Jan 2020
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Quote:
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April 2, 2021, 05:15 |
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#5 |
New Member
Join Date: Jul 2013
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use the boundary point, first and second internal nodes for quadratic interpolation, then calculate derivative at the boundary point
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April 30, 2022, 08:43 |
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#6 |
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Nipin L
Join Date: Nov 2012
Location: Canada
Posts: 23
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Taking the boundary, Phi_P and Phi_E points gives the required formula 5.54. One can check by entering 0,1,3 in the link provided by Denero.
However, considering boundary, Phi_P and Phi_e values, gradient estimate to be (25*Phi_P-22*Phi_A-3*Phi_e)/8 Last edited by nipinl; April 30, 2022 at 08:54. Reason: included answer |
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May 10, 2022, 06:03 |
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#7 |
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Josh Mendes
Join Date: May 2022
Location: UK
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This question is really difficult for me. I can't solve it either. Thanks to your post I already know the answer. Thanks!
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November 26, 2023, 08:34 |
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#8 |
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Manish
Join Date: Nov 2023
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I have not been able to derive equation (5.54) as already questioned by Farhad9 earlier, few posts above. Can someone please share the derivation. Thanks.
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