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Cylindrical NS(FDM) at r=0

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Old   September 18, 2004, 03:17
Default Cylindrical NS(FDM) at r=0
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Hi, I have a question about cylindrical NS equations. They have 1/r*(r*u) terms, which cannot be disretized at r=0. I am using staggerd 2D axisymmetric cylindrical cordination and would like to give value at r=0. I have tried


--1/r*(r*u) = (u - (-u))/dr, (axisymmetric) The program runs, but is it OK? Have you got any suggestion?
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Old   September 18, 2004, 05:17
Default Re: Cylindrical NS(FDM) at r=0
Junseok Kim
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In the axisymmetric cylindrical NS equations, the radial velocity u is zero at r=0.
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Old   September 18, 2004, 08:54
Default Re: Cylindrical NS(FDM) at r=0
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L'hospital rule: u/r = du /dr -> (u(i+1)-u(i))/dr +O(dr^2)
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Old   September 20, 2004, 01:04
Default Re: Cylindrical NS(FDM) at r=0
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goto :

then : Publications

Then : annual research brief 2000

Search fo Lele,

The paper is

A new method for accurate treatment of flow equations in cylindrical coordinates using series expansions. G. S. Constantinescu and S. K. Lele


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Old   September 25, 2004, 04:02
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Thank you for your kind reply. My program is almost complete. But I have one more problem.

I know Vz/r = d(Vz)/dr = 0

but what about Vr/r = d(Vr)/r = ??

Which is appropriate? Vr/r = d(Vr)/r = (Vr(1) - 0)/dr or Vr/r = d(Vr)/r = 0
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