Handling of diffusion flux terms at the boundaries with QUICK scheme
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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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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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use the boundary point, first and second internal nodes for quadratic interpolation, then calculate derivative at the boundary point
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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 |
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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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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