> > >> What do you mean as mean field velocity ? >> To report exactly from his paper what he wrote in terms of displacement >> increment : >> >> delta_u = delta_u(real_vel) + gradVel*pos*dt; (1) >> >> >> where : >> delta_u(real_vel) = vel*dt; (vel is from the real particle velocity, hence >> = a*dt) >> >> So the increment of velocity I guess would be given by : >> >> delta_v = vel + gradVel*pos; (2) >> > Well, to get (2) I just followed the numerical scheme, delta_u is the increment, I do not see why you want to derive it. Anyway, we get _exactly_ the same result at the end (for Cundall solution, I mean).
> >> > Heh, no! If you derive (1) vs. time, it will not give (2). > First, divide (1) by dt to get instantaneous quantities : > > du/dt = vel = du_real/dt + gradVel*pos = v_real + gradvel*pos > (v_real is not "real" at all, it is the velocity in the local coordinates > of the corresponding cell, the real one is the sum) > > The time derivative gives : > > acceleration = acceleration_real + d(gradVel)/dt*pos + gradVel*d(pos)/dt > > first term : comming from contact forces > second term : (grad-prevGrad)*pos (after integration on dt) > third term : convective term. > > The third term blocks elastic waves. That is why I'm not sure which one is > best. HCresize=1 (only first two terms) will gives periodic waves, > HCresize=2 will stop them (I could confirm in simple 1D cases). For slow > deformation, the convective term is negligeable and both gives the same. > mmh, this is interesting although atm I am not very familiar with this kind of problems. Thank you for explanation. Cheers. Chiara _______________________________________________ > Mailing list: > https://launchpad.net/~yade-users<https://launchpad.net/%7Eyade-users> > Post to : [email protected] > Unsubscribe : > https://launchpad.net/~yade-users<https://launchpad.net/%7Eyade-users> > More help : https://help.launchpad.net/ListHelp >
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