appropriate time step

Dear Yamamoto,

TOUGH2 has automatic time step control, which means that time-step size can be reduced OR increased depending on number of Newtonian iterations required to converge.  So you can go ahead and start with a small time step and let the code run and increase time-step size.  Not knowing your problem or anything about it, I would suggest you start with 100 s as initial time step and let the code automatically set the time-step sizes. 

See PARAM.2 and PARAM2.1, 2.2 etc. in the manual.   In short, set DELTEN = -1.   and include on the next line the specification of DLT(1) = 100.   Also make sure MOP(16) = 4. 

The code will start with 100 s as initial time step, and then double the time step if convergence occurs in less than or equal to 4 Newton iterations.  If the code cannot converge in 8 iterations, it will cut the time step automatically.

-Curt

Dear Yamamoto,

if the automatic time step control of TOUGH2 is active, time step sizes will be controlled by the time scale of the fastest state changes. This means that the initial time step size will reflect the fastest transient process at time zero.

The reason why the fastest transient process takes control of the time step size is that TOUGH2 can only solve the differential equations for the next time step if the next system state is not too far away from the current one. Otherwise, TOUGH2 has to reduce the time step size.

Let's put it like this: If you would plot the temporal evolution of gas pressures (for example) at early times, how closely should the supporting points of your graph be spaced in order to achieve a very smooth curve? This spacing will probably be in the order of magnitude of the "appropriate" time step size provided by the automatic time step control of TOUGH2.

If you still observe a problem with your simulation using the automatic time step control, an inadequate value of the initial time step size might not be your actual problem:

Let's suppose, you would choose an initial time step size of 1 year using REDLT=2 (time steps will be divided by REDLT in case of convergence failure). TOUGH2 will stop execution after 25 successive convergence failures, which means that you will end up with a time step size of approximately 1 second. This is a quite large time window, which should cover a good guess for your initial time step size. This time window will grow even larger if you choose the default value of REDLT=4.

Consequently, if you start your simulation with a large initial time step size TOUGH2 should be able to find a good starting value without too many successive time step failures. However, if you find that TOUGH2 nevertheless decreases time steps sizes more than 25 times in succession, we should not conclude that your hydraulic system changes so fast that it requires time step sizes of implausible small magnitude. More likely, there is some other problem in your model setup.

In order to estimate what an implausible small magnitude might be, just divide the expected simulation time by the maximum number of time steps you want to spend.

Martin