Time Varying Maximum Timestep

This post highlights the time varying maximum timesteps command, which helps optimize simulation runtimes while maintaining high temporal resolution during periods of rapid model input changes. The time varying maximum timesteps command allows you to adjust timestep sizes dynamically using a simple time-value table. A sample problem demonstrating this feature, based on the "Abdul" verification model, is available for download. This version refines timesteps during key boundary condition changes, leading to approximately 100 additional timesteps and improved solution refinement.

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Figure 1: Command description

This week we’d like to highlight a command which is useful for optimizing simulation runtimes while maintaining a high level of temporal resolution during time periods with highly variable model inputs (the time varying maximum timesteps command).

Here are a few quick examples of where this might be useful.

Perhaps you are modeling the impacts of freeze-thaw cycles in a region which experiences very lengthy periods under frozen conditions (e.g. >8 months of the year). In this case you may want to use a large maximum time step (e.g. 7 days) to minimize the simulation run time; and on the other hand, you may want to use a much smaller maximum timestep (e.g. 0.5 days) during the spring freshet.

Or perhaps your model has a very long spin-up period under pseudo-steady-state conditions followed by a period with relatively quick and frequent changes to boundary conditions. In this case you may desire long time steps during the spin-up period but shorter, controlled time steps during the period of increased variability.

Fortunately, the time varying maximum timestep command allows you to carefully manage the maximum timestep size throughout your simulation using a simple time value table. Figure 1 shows the Reference Manual entry for the time varying maximum timestep command (see section 2.5.2 for more details, page 78):

This command is demonstrated in a simple sample problem which you can download here: abdul_transport_time varying maximum timesteps.zip

The sample problem is a variation of the Abdul verification problem that is included on installation, but this version also simulates the movement of a solute through the simulation domain. By reviewing the *.grok files included in the problem folders we can see that a rain flux (2 cm/hour) is applied to the top of the model for the first 50 minutes of the simulation, accompanied by a specified third-type concentration flux of 1000 mg/L for 50 minutes. The simulation then continues for an additional 50 minutes, for a total simulation time of 100 minutes.

In the original version of the model (‘abdul_transport_base’) adaptive time-stepping is used to guide the simulation:

!--------------------------  Timestep controls
head control
0.5
saturation control
0.050
newton iteration control
10

maximum timestep
100
initial timestep
0.5
maximum timestep multiplier
2.5
minimum timestep multiplier
0.5

In the time varying maximum timesteps version of the model (‘abdul_transport_time varying maximum timesteps’) we can see that a max timestep of 1 second is imposed on the model for 50 seconds after the rain and specified concentration boundaries are activated and again once they are deactivated (i.e. from seconds 0-50 and 3000-3050):

!--------------------------  Timestep controls
head control
0.5
saturation control
0.050
newton iteration control
10

time varying maximum timestep
	0	1	!initial max timestep of 1 second
	50	100	!after 50 seconds increase max timestep to 100 seconds
	3000	1.00	!max timestep of 1 second after rain flux deactivated
	3050	100	!after 50 seconds return to max timestep of 100 seconds
end

initial timestep
0.5
maximum timestep multiplier
2.5
minimum timestep multiplier
0.5

The Simulation Time Reports for both versions of the model are shown in Figure 2, and as expected the version using the time varying maximum timesteps command has approximately 100 additional timesteps. And finally, to demonstrate the potential impacts of timestep refinement during periods of variability I have plotted the solute concentration at the observation point over the first 100 seconds of the simulation (Figure 3). While the results here are quite similar under both time-stepping conditions, the time varying max timesteps do provide additional refinement of the solution.

We hope this will help you to achieve better/more refined results while maintaining relatively short model runs!

Figure 2: Simulation time reports with/without time varying max timesteps

Figure 3: Solute concentration distribution with/without time varying max timesteps