Time effects in flow simulations are characterized by specific time scales that define the upper limit for the time step used. For meaningful simulation, time steps should be chosen to be about onetenth of this scale or shorter. The optimal grid density is closely related to temporal resolution in unsteady computations. Here, the CFL number (Courant-Friedrichs-Lewy) plays a central role. For efficiency reasons, it is chosen as large as possible but must not exceed 1 in explicit methods:
where:
- xmin= Element size in the local flow direction
- Δt = Time step
- umax= Local flow velocity
A finer grid requires smaller time steps and leads to a higher number of iterations until convergence, even in steady-state solutions or with large time steps. To demonstrate the stationarity of the solution, an additional calculation with a modified, usually reduced time step is necessary.
In quasi-steady RANS calculations with a large time step (false-time-step), there is a risk of capturing a state close to a turning point in the flow pattern rather than the mean value. Figure 6.6 illustrates such a case, where the steady solution represents the turning point of the fluctuating flow instead of the mean. This issue highlights the need for careful selection of time step and grid resolution, as well as a critical interpretation of the results.