[sirpolar]

Dear all
How an I consider the optimum time step size for implicit vof scheme?
Is there any criteria for that or it is enough to converge the solution in each time steps?

[LuckyTran]

The time-step should be short enough for you to resolve any temporal behavior that you might be interested in. If you don't care about temporal behavior as much, then you can afford larger time-steps.

Otherwise, choose a time-step short enough so that the solution converges in 10 to 100 iterations. This is tunable. And is simply a general practice. It doesn't matter much whether you do two time-steps for 50 iterations each or one bigger time-step (2x the original time-step) for 100 iterations, so you might as well do the two smaller time-steps to avoid temporal clipping.

[sirpolar]

Originally Posted by LuckyTran

Otherwise, choose a time-step short enough so that the solution converges in 10 to 100 iterations. This is tunable.

Dear luckyTran
you mean I have to increase maximum iteration per time steps up to 100 or decrease time step size in order to converge all the time steps?
Is it okay if just some time steps get converged?

Is there any difference between the final answers if for exapmle time step 3 second , 20 iteration and time step 6 second and iteration 40 both converge in each time steps?

[LuckyTran]

Originally Posted by sirpolar

Dear luckyTran
you mean I have to increase maximum iteration per time steps up to 100 or decrease time step size in order to converge all the time steps?
Is it okay if just some time steps get converged?

Yes, you need to increase the maximum iterations per time steps or decrease the time step size to achieve convergence at each time step. All time steps need to converge. If only a few time steps do not converge then you can propagate that error through time. If many of the time steps do not converge then you can also accumulate error with every time step. There is no reason for 100, it can also be 1000 or 10000. But you generally do not want to devote too much time to one step, you'd rather step the same amount of time on multiple time-steps.

Originally Posted by sirpolar

Is there any difference between the final answers if for exapmle time step 3 second , 20 iteration and time step 6 second and iteration 40 both converge in each time steps?

For implicit time-stepping and for small time-steps, in principle there should not be any difference. Implicit time-stepping is generally not prone to instabilities. But it is still prone to inaccuracies. The assumption is that your big time-step is small enough to be accurate. That is, there will be temporal clipping of the result of larger time-steps. You may consider going from a time-step size of 1e-5 sec to 5e-6 sec and expect similar results. But don't expect accurate result if you go from 1e-5 to 1 sec.

[sirpolar]

When I use different time step size and number of time steps for a specific time (e.g. 10000 seconds) and in all of them all the solutions converged but the results are significantly different. what should I do and how can I understand which time step are better?
this problem is when i use implicit or explicit scheme too.

[pilakin]

well ... a smaller time step is always better in terms of solution precesion. but also often worse in terms of time for a complete simulation.

if you discover new features and significantly different results with a shorter time step compared to a longer one the long time step was too long.

[LuckyTran]

Explicit time stepping requires less memory and is faster than implicit time stepping, that is because new quantities are calculated explicitly rather than having to simultaneously solve a large system of algebraic equations (inversion of big matrix). Explicit time stepping however is especially prone to numerical stability issues and the time-step size must be limited to small steps that satisfy some stability criteria (usually the Courant number needs to satisfy the CFL condition).

The time-step size for implicit time-stepping can be made arbitrarily large without running into stability issues, however there are still accuracy issues. That is, numerically stable results but not numerically accurate.

Whether explicit or implicit, smaller time-steps generally provides more accurate results.

It is hard to predict beforehand (a priori) how accurate different time-step sizes will be. But qualitatively it is very clear. Consider a dynamic or time-dependent signal/process. Your time-step size determines the smallest resolved frequencies of the system (as per the Nyquist criterion). On the other hand, the total simulated time determines the largest resolved frequencies. These upper and lower bounds on the frequency will determine how accurately you can reproduce the behavior of the dynamic process. Very large time-steps would be analagous to measuring the dynamic pressure using a pitot probe with very long tubes attached between the pitot probe and manometer/transducer.

The question is what are the time-scales of the dynamics of the process and how much needs to be resolved? These time-scales are process dependent. For DNS that would be the time-scales of the smallest eddies. For a stationary process, the time-scale is infinite and any time-step will do.

Unsteady RANS does not predict completely dynamic turbulence. URANS only takes into account the unsteady properties of the RANS part (i.e. the unsteadiness of the boundary conditions) and their impact on the turbulence. Your time-step size should be small enough to resolve the time-scales of the unsteady part of the RANS if you want accurate solutions. e.g. if you have inlet velocity as a function of time, then your time-step needs to be small enough to resolve that. Sometimes the unsteadiness is inherent and not caused by time-dependent boundary conditions, such as vortex shedding. Many times ppl run URANS on a process that is stationary. In those situations, results from all time-steps are the same and any perceived unsteadiness is from numerical inaccuracies.