The kinematic anomaly in MPM

The following Material Point Method (MPM) simulation of sloshing fluid goes “haywire” at the end, just when things are starting to settle down:

130327_watercolumn_GIMP_pID

(if the animated gif isn’t visible, please wait for it to load)

Similar anomalies have been observed in penetration simulations, where a sudden pressure pulse forms in material that had been once deformed severely but is, at the time of the anomalous pulse, now relatively quiescent. The fundamental reason for this anomaly (much less its resolution) remains an open research question, which is why it is being described here in this blog posting.

The problem definition is provided in WaterColumnKinematicAnomalyProblemStatement.pdf.  We challenge (or plead with) the MPM community to articulate proper algorithms that will give realistic and stable solutions to this problem for a range of realistic material property values.

6 thoughts on “The kinematic anomaly in MPM

  1. Hi Rebecca,

    I’m not sure if it is related, but a graduate student and I have been seeing the same sort of thing using MPM. Not in the same type of problem, but one in which very large deformations have occurred for quite a long time during the simulation. Then all the sudden, it explodes! Did you ever figure it out? Anyway, thanks for posting this. Hope you are well!

    Kind Regards,
    Reuben

    • No resolution or rigorous explanation has been brought to my attention (might be the ringing instability talked about in an obscure article by Brackbill? A publication about that is supposed to be submitted soon by Martin Berzins, and I urged him to include this problem in his test suite.) There have been several people who contacted me with their own observations about this anomaly, so it is a great topic for publication. Hope you or someone fixes it!

  2. I’m not a MPM practitioner but several years ago I worked a little in the field of turbulence. I feel strongly, that your problem could be related with the blow-up time problem of Navier Stokes equations. I would check the distribution of enstrophy in the field just before the explosion. I mean, maybe some terms in your method of extrapolating to the grid, make enstrophy to diverge. Is just a possibility. Congratulations for the great work!

    • Sorry that this comment wasn’t seen in a timely manner. Please provide a citation to a journal article that discusses the phenomenon that you are describing, especially the one that details the role of enstropy.

  3. I’m not a MPM practitioner but several years ago I worked a little in the field of turbulence. I feel strongly, that your problem could be related with the blow-up time problem of Navier Stokes equations. I would check the distribution of enstrophy in the field just before the explosion. I mean, maybe some terms in your method of extrapolating to the grid, make enstrophy to diverge. Is just a possibility. Congratulations for the great work!

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