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January 11, 2006, 11:37 
beginner level  CG oscillations

#1 
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Hi, I'm working on a CG solver for NavierStokes incompressible inviscous equations. Its purpose is purely visual. Advection  pressure cycle with some sources. If anyone has some idea about the following problem I would appreciate it. Jacobi relaxation works fine but CG solver produces strange effect, if speeds in scene exceed 46 voxels per frame. Like a frame to frame pulsation, in one frame the speeds are exagerrated, and another almost stopped. Sequence of images, played with every 2nd image, looks roughly continuous. Grid sizes range from 50^3 to 200^3. Basic unprecond. CG solver. Any number of iterations (10200). Can it somehow converge to the wrong solution?


January 11, 2006, 20:17 
Re: beginner level  CG oscillations

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>>>Can it somehow converge to the wrong solution?
Yes, in my experience, the combination of scaling (dx, dy, dt) & flow velocity can push you in 2 directions. Sometimes, what you are observing is a 'mode' change & the solution wants to 'pull itself' towards one, or other mode. This can be as a result of the physics itself, or of the numeric scheme used. diaw... 

January 16, 2006, 06:55 
Re: beginner level  CG oscillations

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Is there anything that can be done, with preconditioning, or more precision (double vs float), or initial guess? Is it inevitable for things as such to happen if pressure/speed values go above some amount? If CG produces this, is it correct to guess that BiCG, or CGNR will behave the same way? Is there any paper on this subject of this alternate solution? _Sometimes_ the oscillations are smaller if number of iterations is set 10x more than usual. Thanks, Peter


January 16, 2006, 09:42 
Re: beginner level  CG oscillations

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Hi Peter,
The solutions are dictated by the physics, bc's & ic's of the problem you are simulating & the NS themselves. Not so much by your choice of matrix solution technique, although a bad one will surely lead to odd results. The traditional approach has been to add convectionstabilisation &/ or artificial viscosity to prevent the solution becoming singular. In my experience, this constrains the flow into a viscousdominated flow mode. It's ok for 'steady solvers' with very viscous, slowmoving flows. There appear to be other forms of flow modes  across the singularity  which require an acceleration term to be present  ie. unsteady flow solver. The modeswitch can happen very, very quickly, depending on the geometry & velocity. This next mode requires some cunning scaling to work through & understand. It isa lot of fun... to be sure. diaw... 

January 17, 2006, 11:43 
Re: beginner level  CG oscillations

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Thanks for your posts, diaw. Ona last thing, please Is there any book or article about this mode change you mention, and is there some other name for it?
Peter PS I'll just post some more recent findings: * CG solution itself looks something like a standing wave, its pressure solution having positive and negative areas (3050 voxes thick), which change in the direction of the wind source, and position of p=0 areas between doesn't depend much on wind speed, or grid topology. With every frame the sign changes on these areas: 1. +++ 2. ++ 3. +++ * if the grid is narrow (example 100*20*200) then everything is ok * if CG solver works on every 2nd frame, and plain Jacobi solver on frames in between, then everything is ok 

January 17, 2006, 18:20 
Re: beginner level  CG oscillations

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Books on 'mode change'... I doubt it... it's new research findings You may very well have standing wave phenomena  these can be a result of the physics, b/c's, i/c's, or of the numerics & discretisation used.
The 'mode change' I refer to can be seen when certain flow structures intersect  there is a sudden change of flow regime, necessitating revised mesh & time steps, for example. This effect is a byproduct of the physics, & the nonlinearity of the NS. In my experience, standing wave phenomena can occur in a physical situation, given the correct b/c's etc... even the old checkerboard pressure situation can represent a physical solution  a wave solution, not a bulkflow solution. Perhaps you could look into your 'spatial sampling rate' a little more. Feel free to email me some pics of your findings & we can discuss offline. diaw... 

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