CFD Online Discussion Forums - determination of time step in transient simulation

I'll try to make it short. The time step in transient simulations is determined by two considerations: numerical stability and accuracy.

Stability may require small time steps, depending on the type of numerical scheme you are using to advance the solution in time. It's typically only an issue with explicit schemes, whereas implicit schemes can handle large time steps.

For accuracy, the time step has to be small enough to resolve all essential flow phenomena. How do you know the important time scales in advance, before even running the simulation? Well, you don't exactly know it, but you should know enough about your case to make a reasonable estimate. For example, to solve the unsteady flow on an oscillating airfoil, you would choose the time step small enough to have a certain number of steps (say 50) within each oscillation period. Likewise, you would want to resolve the motion of a piston in the cylinder of a combustion engine with a resonable number of time steps per cycle. If you're solving a case with intrinsically unsteady flow (like vortex shedding), you need to estimate the dominant frequency (maybe known from experiements) and again choose a reasonable number of time steps per period to resolve the flow. All these cases are periodic in some sense, but even if it's not periodic, you need to know enough to get a ball-park figure of the time step necessary to resolve the dominant time scale.

It should be obvious that the stronger consideration (stability or accuracy) will determine the time step. For example, if your explicit scheme requires a time step of 1 sec, and accuracy demands a time step of 2 sec, you'll have to go with 1 sec. (Implicit schemes are very popular for the reason that you can concentrate on accuracy, without having to worry about stability).

All the above will get you started, but when you are facing a new problem, you will ultimately perform a (grid and) time resolution study, i.e. use various time steps, around the order of magnitude of your initial estimate, in order to find the actual requirements. You may sometimes be surprised by a flow phenomenon you did not expect.