Hi, I'm working on a CG solver for Navier-Stokes 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 4-6 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 (10-200). Can it somehow converge to the wrong solution?

>>>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...

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

Hi Peter,

The solutions are dictated by the physics, bc's & ic's of the problem you are simulating & the N-S 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 convection-stabilisation &/ or artificial viscosity to prevent the solution becoming singular. In my experience, this constrains the flow into a viscous-dominated flow mode. It's ok for 'steady solvers' with very viscous, slow-moving 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 mode-switch 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...

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 (30-50 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

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 by-product of the physics, & the non-linearity of the N-S.

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 bulk-flow solution.

Perhaps you could look into your 'spatial sampling rate' a little more.

Feel free to e-mail me some pics of your findings & we can discuss off-line.

diaw...