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Why does the non-orthogonal term in FVM need to be evaluated explicitly? |
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#1 |
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Yu Wang
Join Date: Sep 2021
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In FVM, the face normal gradient is split into orthogonal and non-orthogonal part. The orthogonal part is evaluated implicitly, whereas the non-orthogonal part is evaluated explicitly as a source term using known velocity field. My question is why is the non-orthogonal part not implimented in a way such that it is evaluated implicitly? Is there any advantage in the explicit implimentation?
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#2 |
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Filippo Maria Denaro
Join Date: Jul 2010
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Could you better details your question with an example to a textbook/paper?
I suppose your are talking about FV on unatructured grids. |
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#3 | |
Senior Member
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Let's bypass the difficulty in tracking the coefficients with all the different methods and go straight to the point: you get an enlarged system band getting higher memory consumption, less cache efficiency and reduced diagonal dominance as you put in second layer neighbors. Deferred correction is just simpler and works better. |
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#4 |
Senior Member
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Now let me highlight that tracking the coefficients for general methods is a real difficulty. For example, in my code I have a method where a weighted least squares gradient is used as initialization for a green gauss method. It's not impossible but nothing I want to deal with in a general purpose CFD code.
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#5 | |
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Sayan Bhattacharjee
Join Date: Mar 2020
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Quote:
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#6 | |
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The issues are the book keeping to derive the exact coefficient formulas for each gradient method (and, as I wrote, some methods would be very challenging to derive, imagine debugging) and the matrix diagonal dominance in serial as well parallel. More off diagonal terms is bad for diagonal dominance independently from the parallelization. Even a single layer least squares gradient (which is super easy for the coefficients, because you already have them) still increases the number of layers by 1. |
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