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Carlos August 26, 2007 19:04

Epsilon Convergence Trouble

I am simulating airflow over a vehicle using the realizable k-epsilon turbulence model on a grid of ~ 8 million cells. I am using a hybrid grid of hex and tet cells and the simulations are second order.

For slow air speeds I get satisfactory convergence, however for faster speeds I have trouble with the residual levels for epsilon. All other residuals are converged ok (below 10^-5) and everything levels off after 6000 iterations. Epsilon does level off too, but there is a medium amplitude oscillation present and the average residual value is around 10^-4.

I have tried relaxing the solution which helps generally but epsilon is largely insensitive. I tried lowering the under relaxation factor for epsilon from 0.8 to 0.6 but this has little or no effect.

Any ideas or secret recipies for improved convergence with this turbulence model? Many thanks,


AAA August 27, 2007 01:55

Re: Epsilon Convergence Trouble

I think you've nailed the problem Carlos. With 8 million cells and such low residuals after 6000 iterations, you are my man. But what velocities are we talking here?

Carlos August 27, 2007 07:40

Re: Epsilon Convergence Trouble
Hi Triple A,

In terms of the appearance of the residuals yes I do have a converged solution, however I'm not entirely happy with the residual level for epsilon. I have read many times that the default convergence limit is 10^-3 and this is not enough for 3D problems. As an absolute bare minimum these days I try to get everything below 10^-4. Usually with k-e models everything plays ball except for epsilon.

I am using a velocity of approx 22m/s which is about 50Mph. The flow is both internal and external as I am looking at ventilation in livestock trailers. Does anybody know of any other method other than altering the relaxation of the solution to get lower residuals? Is it worth looking at Multigrid methods to try and lower things? It just seems like something which takes a long time to set up. And am I correcting in thinking that Multigrid simply SPEEDS UP convergence and doesn't actually help the convergence levels?

Maybe I am just being paranoid here but I am trying to be as rigorous as possible in writing a paper for a good journal. Thanks for your time. All the best,


Dusan August 27, 2007 08:20

Re: Epsilon Convergence Trouble
it is truth, it has to be at least half of cells, i think

AAA August 27, 2007 11:22

Re: Epsilon Convergence Trouble
Hi Carlos,

I usually have slightly lower residuals when I perform adaption. Try performing adaption on velocity gradients and see if this helps.


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