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Corner nodes and neumann bc

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Old   March 29, 2008, 15:31
Default Corner nodes and neumann bc
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Hi everybody,

I'm trying to find the correct discretisation with finite differences of a neumann boundary condition at a corner node.

As an example:

dpdx = f1(x,y) and dpdy = f2(x,y)

So how to apply them in a square cavity for the node (0,0)

It's obvious that we can't apply only one of them, nor both...

If you have any idea or a reference that gives a clue, thanks in advance.
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Old   March 29, 2008, 20:36
Default Re: Corner nodes and neumann bc
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If you want to be exact, there are solutions based on perturbation methods which account for the exact corner node. For other problems, the application of BC depends on how you discretize. Regarding the cavity problem, there was a paper long ago by goldstein ( may be wrong name ? ) which discusses the issue of applying the boundary condition at the corner node.
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Old   March 31, 2008, 07:21
Default Re: Corner nodes and neumann bc
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Thanks for your answer, but could you give me some references about the use of the perturbation methods in cfd... Also, I found no paper related to Goldstein on the cavity problem...

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