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I have a transient flow and solute transport simulation running using a fortran code. The final solution time is 1 day. I need the output of hydraulic head for the output time of 0.5 day. I want to know what is going to change in my output data (0.5 day) if I run the same simulation for a longer time, e.g., 1000 days?

I know the system will get closer to steady state, but how will it affect the data for the output time that I want (0.5 day)?

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    $\begingroup$ If you are solving your problem as a system of ODE's (which is common for most fluids problems), running the code past the point of interest will not have any effect on your answer. $\endgroup$
    – Godric Seer
    Apr 25, 2013 at 19:07
  • $\begingroup$ @GodricSeer I think the system of equations consist of PDEs for transport coupled with AEs for chemical equilibrium. $\endgroup$
    – Mary Jane
    Apr 25, 2013 at 19:19
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    $\begingroup$ If you are solving the PDE's on a mesh, then they are being reformulated as a system of coupled ODE's. If you need the answer AT 0.5 days (whether or not it is steady state), you should run to 0.5 days. If you need the steady-state solution, look to Jed's answer. $\endgroup$
    – Godric Seer
    Apr 25, 2013 at 19:40
  • $\begingroup$ Yes, I have a mesh set up for my problem. I need the output at the early simulation time (0.5 day) when system is transient. $\endgroup$
    – Mary Jane
    Apr 26, 2013 at 7:45

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There is no way to know how far from steady state a nonlinear transient simulation is. Indeed, many famous ODEs (e.g., stiff Van der Pol or Robertson test problems) have arbitrarily long periods of nearly-stationary behavior before changing rapidly and repeating the process. If you add some dissipation, the system may or may not undergo the eventual large change, depending on parameters.

If you have an implicit solver, you can solve directly for steady state, if such exists. (See papers on "pseudo-transient continuation" to help globalize and to ensure that you find a physical steady state.) If the system eventually enters a limit cycle, you can also solve for the limit cycle (though this is more challenging).

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  • $\begingroup$ The code uses global implicit solution technique. I think in real experiment, the soil system gets to a pseudo-steady state condition after long time of infiltration, however, I am also interested in the transient part that happens at the early time of simulation. $\endgroup$
    – Mary Jane
    Apr 26, 2013 at 22:08
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Nothing will change as long as all the other parameters remain the same.

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