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[Jérôme Duriez <question267815@xxxxxxxxxxxxxxxxxxxxx>]

Question #267815 on Yade changed:
https://answers.launchpad.net/yade/+question/267815

    Status: Open => Answered

Jérôme Duriez proposed the following answer:
There is probably different possible ways answering your question..
Hoping that others won't be too much different, here is a first one.

As for the time dependancy, I guess you re speaking on timestep, isn't
it ? You may give a look to Figure 1.19 of [Duriez2009a] (my PhD thesis,
sorry..) on https://tel.archives-ouvertes.fr/tel-00462072/document

No need to understand french, it shows the mechanical (kinetic + elastic) energy of a mass-spring system. This system is simulated using a Finite Difference scheme quite similar to "Yade's one", and energy data are plotted according to timesteps.
As you can see on the Figure, the discrepancy with respect to the constant initial value corresponding to theory (thick "Theorique" line) increases with the timestep.

As for myself, I consider this as related with an approximate nature for
computations done within DEM (as with any numerical method), with
velocity and acting forces being constant throughout time intervals
corresponding to one timestep. Leading to approximated energy balances.
(dW = f . v dt is not equivalent to W = ExtremeValueOfF .
ExtremeValueOfV . DeltaT)


You may have another point of view, though.. Considering that the discrepancy arises from using values that do not correspond to the same time, with e.g. velocity values being associated to the middle of a time interval (at t = t_i + DeltaT / 2), while positions correspond to t = t_i or t_{i+1}. Which may allow to be consistent with theory.
Other people could probably elaborate this point of view better than me   ;-)

As for me, I do not feel so much at ease with this point of view, since
I think the half of the timestep (DeltaT / 2) never enters in Yade
computations (as in any other DEM code ?)

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