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Automatic time stepping

The use of automatic time stepping is strongly recommended in most applications. The number of numerical parameters and the risk of numerical instabilities are reduced. Optimum performance is achieved by automatically choosing the highest stable time-step value.

There are two independent criteria for automatic time stepping: a pure phase-field criterion and a segregation criterion. Both are stability criteria. The simulation usually gets numerically unstable if a too large time step is used.

According to the phase-field criterion, the time step must not exceed a critical value, depending on the spatial resolution \Delta x, the surface energy \sigma and the interface mobility \mu. The segregation criterion is only relevant in case of concentration coupling and depends on the redistribution thermodynamics.

For both criteria, a pre-factor can be defined as optional parameter in order to allow manipulation, a value of 1.0 exactly corresponds to the criteria shown above.

The resulting effective phase-field time-step as well as the time-step values of the individual criteria can be monitored in the TabT output. Due to the fact that a worst case scenario is used for the segregation criterion, in some cases a pre-factor >1 may be still acceptable and could even increase substantially the performance of the whole simulation.

The drawback of the worst-case scenario for the segregation criterion is that the behaviour of one grid cell may affect the time-step and thus the performance of the whole simulation. If one single interface cell experiences a numerical problem and combined with unreasonable thermodynamic parameters, this single cell could extremely decrease the global time-step. This can practically freeze a simulation. The solution is the definition of a minimal time-step which can be specified as a third optional parameter to the automatic keyword. If a minimal time step is used, the interface mobility \mu of those (exceptional) cells which would need a smaller time-step than the minimal one is reduced. One should check the mueS output to make sure that this does not happen for too many cells.