[Nek5000-users] Periodic BC on non-parallel boundaries

[nek5000-users at lists.mcs.anl.gov]

Hi David,

I was using a similar transformation for the annulus except for the order of r & theta, i.e. I mapped [r,theta,z] -> [x,y,z] preserving right-handed coordinate system...

Aleks

----- Original Message -----
From: nek5000-users at lists.mcs.anl.gov
To: nek5000-users at lists.mcs.anl.gov
Sent: Tuesday, October 11, 2011 3:03:16 PM
Subject: Re: [Nek5000-users] Periodic BC on non-parallel boundaries


Hi Stefan, 




What do you mean by "remapping a periodic-side domain in userdat2"? 


I build a mesh using genbox with dimensions [0,1]^3. The BC are periodic in x. Then in userdat 2 I remap the (x,y) cross-section from a square to an annulus: 

call rescale_x(xm1,zero,pi2) 
call rescale_x(ym1,zero,one) 

n = nx1*ny1*nz1*nelv ! Turn box into annulus 
do i=1,n 
th = xm1(i,1,1,1) 
r = r0 + (r1-r0)*(1.-ym1(i,1,1,1)) 
xm1(i,1,1,1) = r*cos(th) 
ym1(i,1,1,1) = r*sin(th) 
enddo 

This gives me an annulus centered on the z-axis with interior radius r0 and exterior radius r1. (I tried centering it on the y-axis instead with the periodic boundary lying in the xy-plane, but the result was the same.) My velocity BC in what are initially the y and z directions are all SYM, so I need to use the stress formulation. 

This procedure worked in 2D for no-slip or stress-free BC, but in 3D it is not working for stress-free BC. I can visualize the 3D geometry, and the annular cylinder appears to be properly constructed, but the fluid solution blows up. 

I understand now that my fractional-annulus cases blow up because non-cyclic periodic BC at the theta-ends are incompatible with stress-free walls, but this should not be an issue for the full 2π annulus, even in 3D. Can you think of a reason that non-cyclic periodic BC would work in 2D but not in 3D? 



Sure, even with IFCYCLIC=F you'll get a result. But is probably not 
the one you had in mind, simply because the BCs are different i.e. 
periodic vs cyclic. 


Ah yes, you`re right that the results are actually different. 

Thanks a lot, 

David 

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