# When to stop calculations?

Hi,
I apply the LBM to the 3D lid driven cavity test.
How to define that steady state is reached?
It is obviously possible to check a condition as max|(usup[/sup]-u[sup]n[/sup])/u[sup]n[/sup]| < eps where
|u[sup]n[/sup]| > 0 and n is time index.
Are there any more correct and economic ways?
Thanks.

Just an idea
check a few points (4-8 maybe) and if all of them u(x,t+1)-u(x,t)<condition then do the max check as well and if thatâ€™s true as well --> steady state

Thanks. And similarly to do the check not on each time step but through 10-20 steps.

Exactly =) any good results?

But do You think that is enough to check max difference ??
As far as I know one of the way is to check
[ sum |(u[sup]n+1[/sup]-u[sup]n[/sup])| / sum (|u[sup]n+1[/sup]|) ] < eps

I usually compute the change of velocity on the entire grid, but I only do it every, say, 1000th time step (and I increase the threshold epsilon by a factor of 1000). This way, one has an accurate check more or less equivalent to checking each time step with epsilon. However, it is less expensive in terms of computational costs. Until now, I was always satisfied with the results.

But do You compute the max difference on the entire grid or sum of all differences ?

sum of all differences, quadratically weighted so that no deviations can cancel each other