Hello dear Dumux community,
I'd like to ask 2 question:
1) how it is discretized an equation like: du/dt = - du/dx in Dumux. Of
course, I'm not asking for the all course of numerical discretization of
PDF, but the specific solutions which are implemented in Dumux since I
noticed that even if apparently simple equation, it is not always well
handled by solvers and it may represent a major flaw in the simulation
of viscous fingers for example.
2) Secondly, how it is handle the mixed nature of the PDE in Dumux.
3) I'm wondering, simulating highly unsteady and unstable scenarios such
as viscous fingers, how can I trust my solution? I mean, which
mathematical/numerical means I can use to assess a certain level of
confidence of my solution. In general, I would look at some norm, by
performing some grid convergence analysis and error estimate, for
example the Richardson extrapolation on multiple grid levels.
Nevertheless, it is knows that viscous fingers are quite hard to
simulate, since they look different on different grid refinement levels
and topolgies. Thus, how can I say that what I see is "close" to the
real physics, at least in some approximation?
Thank you,
Kind reagrds,
Lorenzo Campoli
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