yade-users team mailing list archive

[chiara modenese <c.modenese@xxxxxxxxx>]

2010/5/6 Václav Šmilauer <eudoxos@xxxxxxxx>

>
> > I am playing a little bit with the code to understand how thinks work
> > in terms of energy. I started with a very simple example of two balls
> > in normal contact.
> > I am only applying an initial velocity to one particle, hence the
> > total energy of the system is only given by (kinetic + potential
> > elastic).
> > Look at the two attached figures. The first one (dt_crit) is the
> > result obtained using the critical time step computed by Pwave in
> > Yade. The second one (dt_Econst) is obtained decreasing the time step
> > to get the total energy constant.
>
> Hi Chia, very nice plots. What were values of Δt in there two cases? Or
> rather, what was the Δt_Econst/Δt_crit ratio? (PWave is only an
> estimate; there is a section on that in my thesis)
>

Hi Vaclav,
the two time steps were 9e-8 for dt_Econst and 4e-6 for dt_crit. I am not
doing any criticism on the way the time step is estimated in PWave (in PFD
there would be the same kind of result, for instance, and not using PWave).


>
> What is also interesting that in both cases Etot has eventually the same
> value.
>

The total energy remains the same in both cases because the output velocity
of the particle is the same as the input one (no energy dissipation is
included). BUT this is only a very simple case and the contact is only
created once. The discrepancy that arises in the computation of mechanical
energy might conduct to a different total energy depending on the time step
used (I am pretty sure this would occur running a simulation with many
bodies and for many iterations adopting different time steps).

What I am only trying to point out is that to me choosing the time step that
leads to a numerical convergence it seems to be not enough. This assures a
stability of the numerical scheme but then whether it gives the wanted
precision or not depends on the problem of study. Perhaps I guess that
dealing with _quasi-static conditions_, energy considerations become
superfluous (that is maybe why nobody here has approached the problem?). On
the other hand, if the problem is _dynamic_ I think they matter.

cheers, Chiara



>
> > Now I see that the time step influences the solution in terms of
> > energy and this is just a very little example (so it does not really
> > quantify anything). However, I have one consideration: does this mean
> > that we are mainly dealing with non conservative systems in our dem
> > simulations? Is this the right way to compute the total energy? I
> > guess what happens in a system with many bodies (I am gonna try)..
>
> Speaking of myself, I never measured the energy. Besides fear of never
> getting constant total energy ;-) I was mostly using some fixed
> particles, viscosity etc and didn't bother to compute energy
> dissipation.
>
> Doing this kind of studies might be tremendously useful, though. I am
> sure it will reveal a whole pile of physically questionable things.
>
> Best regards,
>
> Vaclav
>
>
>
>
>
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