OGS
[case] IterationNumberBasedTimeStepping

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 previous 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 previous time step.

Num. of Newton steps0-23-67-89<
Time step size multiplier1.61.0.50.25 (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.

Note
In the staggered coupling scheme the controlling iteration number is the maximum over the number of global coupling iterations of the previous time step and the number of nonlinear (Newton-Raphson or Picard) iterations of all coupled processes.

Reference

  • Hoffmann J (2010) Reactive Transport and Mineral Dissolution/Precipitation in Porous Media:Efficient Solution Algorithms, Benchmark Computations and Existence of Global Solutions. PhD thesis. pp82. Friedrich-Alexander-Universität Erlangen-Nürnberg.

Child parameters, attributes and cases

Additional info

No additional info.

Used in the following test data files