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OGS
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Iteration number based adaptive time stepping.
This algorithm estimates a time step size depending on the number of iterations (e.g. of iterative linear solvers, nonlinear methods, partitioned coupling) needed in the last time step (see Hoffmann (2010) for Newton-Raphson case). The new time step \Delta t_{n+1} size is calculated as
\Delta t_{n+1} = \alpha \Delta t_n
with the previous time step size \Delta t_{n} and a multiplier coefficient \alpha depending on the iteration number. Note that a time step size is always bounded by the minimum and maximum allowed value.
\Delta t_{\min} \le \Delta t \le \Delta t_{\max}
For example, users can setup the following time stepping strategy based on the iteration number of the Newton-Raphson method in the last time step.
| Num. of Newton steps | 0-2 | 3-6 | 7-8 | 9< |
|---|---|---|---|---|
| Time step size multiplier | 1.6 | 1. | 0.5 | 0.25 (repeat time step) |
| Upper and lower bound | 1. \le \Delta t \le 10. | |||
A time step size is increased for the small iteration number, and decreased for the large iteration number. If the iteration number exceeds a user-defined threshold (e.g. 9), a time step is repeated with a smaller time step size.
Reference
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