On 29.07.19 10:31, lc wrote:
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.
Hi Lorenzo,
the discrete equation, as implemented, is described in detail in the
handbook (https://dumux.org/documents/dumux-handbook-3.0.pdf) sections
6.2/6.3. The discretization methods follow the current literature and
are tested and benchmarked, as documented in multiple publications. If
you have any suggestion on how to improve it, please let us know.
2) Secondly, how it is handle the mixed nature of the PDE in Dumux.
You'd have to be more specific here for us to be able to answer. Which
part of the simulation are you interested in? Which model are you
interested in? Which "solver"/scheme are you interested in? IMPES or
fully coupled? Are you only talking about boundary conditions?...
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?
Please understand that we only answer Dumux-specific questions on the
mailing list and not general research questions.
Best wishes
Timo
Thank you,
Kind reagrds,
Lorenzo Campoli
--
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Timo Koch phone: +49 711 685 64676
IWS, Universität Stuttgart fax: +49 711 685 60430
Pfaffenwaldring 61 email: [email protected]
D-70569 Stuttgart url: www.hydrosys.uni-stuttgart.de
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