I'm numerically solving continuity, momentum and energy equations for imcompressible flow. The scheme is one order accurate both in time and spacing. Theoretically, the decreasing grid size will give the more accurate results as long as the CFL condition is satified. But when I used large number of grids, the unexpected results of oscillation come out. Could anybody explain why this happen? I don't think the CFL is the reason. Is this common?

It is nonlinear instability, stability of your scheme was analyzed for linear equations where CFL is enough, when you increse number of cells, number of steps is increased and the influence in regions of big gradients is essential and it destroys ths solution

It sounds like your grid size is now minimizing numerical viscosity to the extent where you're resolving transient flow features which normally manifest themselves as periodic variation in residuals. A coarser grid would have sufficient numerical viscosity to damp out these transient features.

To check this, monitor the solution of a velocity component at the point of the max residual error, you might see this velocity oscillating periodically as well.

Thanks a lot, it's quite enlighting. any reference concerning these topic?

No, just my experience!

find Quirk's article "Debate on great Riemann solver..." or try search "carbuncle phenomina" problems are similar m.a.

I'm trying to understand the logic in previous postings that with increased mesh density, that the 'diffusive effects' of the large mesh is removed & that the 'true' underlying flow filed begins to emerge - leading to oscillations.

Is there perhaps a chance that with increased mesh density, that numerical errors could begin increasing - leading to oscillations?

Or, is there perhaps something inherent in the FV technique that could contribute to these issues? This last comment is based on conversations with colleagues involved in FEM work who noted that in comparason studies against St**-CD, as the mesh desnity was increased, that the error began to also increase. They attributed this in part to the 'checkerboard scheme'.

diaw...

Hi diaw,

I'm quite interested in your last comment. Can you please explain a bit more of how the checkerboard scheme could cause such residual oscillation? I get similar problem in some cases where I try to use the more sophisticated turbulence model (RSM) and so I agree with you that the diffusive effect could have cause such a problem.

hmm....It seems to deal with gas dynamics & high speed flow where shock wave may occur...Sounds like different stories for me..Haven't fully read through it anyway. The turbulent model used could have contributed some instabilities to the solution as well.

Pete,

The thing that has always concerned me with the use of staggered grids is that solutions are occuring which are essentially offset from each other. The u,v,w velocity & scalar fields are calculated & only interlink via interpolations between their nodes - say at the cell faces of the scalar cell. Often, I have seen that a simple arithmetic average is used to obtain face fluid properties - eg. a central-difference approach as applied to the property itself. What happens when the property is itself varying?

We are also dragging the pressure field up with us as we settle the velocity field. The techniques for doing this are, in themselves, subject to approximations & reliance on iteration to solution. With more iteration comes the risk of additional numerical error.

I have always inherently felt that there was scope for problems at some point.

With collocated schemes, with everything being calculated 'in syncronous' in one cell, I feel that there is less potential for long-term intrinsic instabilities to occur.

One must also not forget, that the basic Navier-Stokes equations upon which we so stringly depend - are in themselves subject to approximations & simplifications. My inner feeling is that we have simplified out the inherent natural damping present in true fluids & now are becoming slaves to false sources of damping to settle the solutions.

The experts in our community can possibly shoot holes in my arguments - but, these 'personal feelings' are based on deep investigations & numerous simulations.

------------- The colleagues I refered to in the FEM community rely heavily on multi-grid techniques & error-estimation. In the early days of the project they evaluated as many schemes as they could obtain data for. St**-CD was burned in their memory for its increasing error with decreasing mesh-dimension (increasing mesh density).

diaw...

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Hi,

I have a similar experience with my solution. I am trying to model bubbly flow in an upwardly pipeflow. When I have 10 nodes in radial direction I observe lesser number of oscillations in the solution where as when I increase nodes to 15 and 20 it becomes worse. Well what I infered with little reading is the pressure velocity coupling in FLUENT needs to undergo revision. One can refer paper by Kunz et al., (1997)where some similar behaviour is discussed. However for an end user it might be a bit hard to implement his reccommendation, as one has to tweak and modify the source code which might not be possible with UDF.

CITATION: Kunz R. F., B. W. Siebert. W. K. Cope, N. F. Foster, S. P. Antal and S. M. Ettore, " A Coupled Phasic Exchange Algorithm for Three Dimensional Mutli-field Analysis of Heated Flows with Mass Transfer", Comp. and Fluids 27, 741-768 (1998). LINK TO THE PAPER

http://www.sciencedirect.com/science...&_coverDate=09%2F30%2F1998&_cdi=5694&_orig=search&_st=13&_sort=d &view=c&_acct=C000051270&_version=1&_urlVersion=0& _userid=1069263&md5=34214d96d9ea71a0f7ab620b036441 ab KP

I think you have it the wrong way round. For convection dominated problems the usual FE arrangement or FD/FV scheme which stores velocity and pressure in the same location has too many unknowns. The staggered arrangement reduces the number of velocity components so that we have the same number of unknowns as equations.

In order to see the above consider the 1D mass and momentum equation for incompressible flow with 2 cells/elements and central differencing for the convection term and no diffusion term.

The result of too many unknowns in collocated schemes is the checkboarding/uncontrolled modes/... or however one wishes to describe it. The solution is to add something unphysical such as pressure smoothing, momentum averaging, biased differencing,... or the like.

The staggered arrangement was designed - as I understand it - to get around the 'checkerboard pressure field' problems...

Refer to Versteeg "An introduction to computational fluid dynamics - The Finite Volume Method" - Chapter 6 - pg 136+ The description & workings are well laid out.

Then move onto discussion of the Simple algorithm etc - pg 142.

diaw...

Hi,

Can you please pass me the full details of Kunz et al paper?

Thanks.

Pete,

Here is the citation;

Kunz R. F., B. W. Siebert. W. K. Cope, N. F. Foster, S. P. Antal and S. M. Ettore, " A Coupled Phasic Exchange Algorithm for Three Dimensional Mutli-field Analysis of Heated Flows with Mass Transfer", Comp. and Fluids 27, 741-768 (1998).

Let me know if u do not have acess to it.

KP

I would concur that the pressure-coupling issue can be a problem in many FV schemes. This is what I was alluding to in a previous post.

Thanks for the paper link.

diaw...