convergence test

Hi Dear All,
Can any one tell me , how we can find that how much maximum iteration steps required for the steady state solution. I mean i want to know if i put the convergence creteria in the code and asssigning (e.g., 500000 time steps) but that’s possible that after completion the convergnece creteria not meet. So can any one would like to tell me how to know that we need such maximum time steps for steady state solution. Thanks in advance and bye for now.

One way to find out how many time steps are needed until steady state is to compute the momentum diffusion time.
It is

t_D = L^2 / (8 \nu)

where L is the length scale of your system (in lattice units) and \nu is the kinematic viscosity (also in lattice units). However, I have found that this definition is very crude and may have to be adjusted depending on the actual problem. Especially the factor 1/8 may be larger in many applications.
What I do to make sure that I have steady state: Every say 500 time steps I check the difference of the velocity profiles at times t and t - 500. If the averaged difference (I compute it similar to the L2 error) falls below a critical value (you have to find an appropriate value), my simulation is finished.

in practice what you can do is to check for the standard deviation of mean quantities (average energy for example). It is the approach used in OpenLB. You can indeed compute it without any real cost in terms of computations since at each time step you have to compute the norm of the velocity. This method would be a bit less expensive. Then you just put some arbitratry threshold to stop the simulation.