Variation of results in SS and TS

Sometime you have a model that converges in SS, that has nice looking heads, but that is not that correct:
- If you run multiple times the exact same model, with different initial heads, you may find different results. In my case I found that the difference is rougly +/- 5 to 10 cm, depending on the nodes (with heads ranging over 30 m).
- In "steady transient" (steady bcs, transient run, high initial heads), heads converge globally toward some "making sense values" however they can fluctuate by an order of several meters, especially at wells but not only.

My model is a phreatic one. What are the rules of thumb to interpret this kind of results ?

Such a model behavior indicates an oscillating result. In steady-state, you obtain a possible result depending on the initial conditions (which are the last result in case you have not re-loaded the model). In transient, you can actually see these oscillations over time, which can be very helpful to identify the parts or features of the model causing the instability. In phreatic, the most common reasons include:
- Relatively high infiltration into dry layers on top which will have very low hydraulic conductivities if they are thick and the default residual water depth of about 1 mm is kept
- Pumping wells that fall dry (dry wells are turned off, the turning off can cause a re-rise of the water table, the well is turned on again, etc.)

Thanks

One questions then:

We can logically reduce the fluctuations by constraining the time steps size. Is there a rule of thumb to say that a certain time step size is still ok in this method ? Not sure if I am clear ... e.g. the model starts to fluctuate when time steps reach sizes > 100 days. If I constrain the time steps to 50 days I reduce significantly the fluctuations. However I am not sure if this is a reasonable approach and if I can validate the model by doing so. After doing so I can run the model in SS, one or two times, after which the convergence is failing again.

In our case we effectively see that fluctuations are more important at pumping wells or along some specific recharge locations (e.g. foothills recharge). However a naked model (no internal bcs) still fluctuates (fluctuations are less important but still exists). We then believe that the geometry combined with the K distribution is the main reason for having such oscillations, but we have difficulties to see how to get rid of the problem (e.g the geometry and K are realistic, the border bcs are very simple constant heads).

Instead of setting an upper limit for the time-step size it might be a better approach to reduce the error tolerance of the model. This will lead to smaller time steps and makes the results of the non-linear iteration (the calculation of the result of the individual time step) more accurate at the same time.
The error criterion is a relative value that relates to the maximum occuring value (initial condition or boundary condition) of the process variable (e.g. hydraulic head for the flow simulation of Temperature for heat transport simulation). If this max value is 100 m, an error criterion of 0.1e-3 would lead to a (probably) acceptable absolute (mean-square) error of 0.1 m. Of course, depending on the model purpose a smaller valuer might be necessary.