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explicit 2nd order scheme


Re-sent to users list. Sorry for doublets.

Jerome Duriez a écrit :
And how are velocities (in both schemes) computed ?

If they are computed by the same mean, I can still not understand at all what is the difference between these two shemes, except the fact that "2nd order" sounds more serious than "1st order"...


In first order scheme, you would use current velocity for p(t+dt) = p(t) + v(t)*dt, THEN you would compute v(t+dt)=..., in 2nd order, you use the updated (second) value instead. A while ago, Yade was using the 1st order scheme for rotations, and it was the reason why we needed so small time steps.

It seems many people have problems with this simple 2nd order explicit scheme. I send the equations in the attached file, with time step determination. I hope (should I?) it will stop endless discussions in my office about this. ;)

You will find the exact same scheme in any Cundall's paper, even if he doesn't explain it exactly the same way perhaps. You will not find the "leap-frog" naming in Cundall's papers though, and personnaly, I don't know what leap-frog is. I only know "explicit 2nd order finite difference scheme", and this is what's in Yade.



Chareyre Bruno
Maître de Conférences

Grenoble INP
Laboratoire 3SR - bureau E145
BP 53 - 38041, Grenoble cedex 9 - France
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Attachment: note.pdf
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