Hello!

I’m working with step-21 in deal.II and I’m trying to perform a *sensitivity 
analysis* based on *saturation front position* (S_front). Specifically, I 
want to compare the simulated front position against experimental data by 
computing the *absolute error in the x-position* of the front at a given 
time.

For example, in my experimental result, the front reaches *x = 5* at *time 
t = 0.265*. The simulation domain is a 2D rectangle of size *30 × 4*, and 
I’m solving a two-phase flow problem with saturation S as one of the 
components.

My goal is to run simulations with different boundary pressure values and, 
at a specific time step (e.g., t=0.265), find the location where the 
saturation front exists, and compare it to the experimental position.

What would be the best practice in deal.II to compute the x-location of the 
saturation front at a given time?

Any advice or pointers would be greatly appreciated. I'm happy to share 
snippets of my code or experiments if needed.

Thanks in advance!

Best regards,

Aibike



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