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[Bruno Chareyre <1734653@xxxxxxxxxxxxxxxxxx>]

>I am particularly confused by [3]

A local crack is a polygonal face of the Laguerre graph. I did not find online content showing a Laguerre graph in 3D but you can find inspiration by looking at a Voronoi graph [1] (some polygonal faces are visible on the outer contour).
The code at [3] is looping on the edges of the polygons, which means algorithmicaly a loop on all  cells incident to a particular edge of the triangulation (each triangulation cell is the dual of a Laguerre vertex).
A wise definition of the "width" of the crack should account for this geometry more accurately (currently the width is just the distance between to points of the polygon). 
It would also lead more naturally to an increase of the conductivity for multiple cracks in one cell.
Your code Robert is doing something along this line (you take from the polygon a triangular subdomain), however you apparently neglected the fact that there are not just two cells associated to a cracked edge, there are many of them. So you need a loop somewhere.

[1] http://math.lbl.gov/voro++/about.html

>It's as if we are artificially creating volume space that is not reflected
by the packing geometry. Which is kind of what this all boils down to,
right?

I don't think so. Instead the algorithm is relying strongly on the idea
that the volume changes are exactly reflected by packing geometry. This
being the case we know the cracked volume without a need to distinguish
the number of cracks and their openings. Calculating volume changes is
not an issue at all, as mentioned in the bug report. The only problem is
for the reference volume used in the compressibility equation (where
"reference" means "before any crack").It is enough to define it once
since later it can always be updated by using the volume change of the
cell (hence no need to consider sums over n or 4-n cracked edges).

You guys have been progressively diverging from the bug, and now I'm following you. ;)
The questions on tricking permeability are completely independent, calculating volume changes as well, let's leave the bug alone and continue in a different thread. To delineate the bug, the question here is:
"what the initial amount of fluid before any cracks should be?"

B

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https://bugs.launchpad.net/bugs/1734653

Title:
  DFN+fluid compressibility not using the correct reference volume

Status in Yade:
  New

Bug description:
  In the basic PFV scheme the incremental change of density of a pore
  fluid after a change of pore volume is dependent on dV/Vo where Vo is
  the reference pore space within a tetrahedral cell [1], i.e.
  V(tetrahedron)-V(spheres).

  In DFNFlow "V" should reflect the fact that porosity may be mainly due to a crack an its opening.
  Typically V=V(tetrahedron)-opening*area-matrixPorosity.
  Currently it is using the same formula, hence overestimating the compressibility effect (because the DEM porosity is larger than a typical rock porosity). What should be the reference "opening" in above formula is to be clarified though, it has physical as well as numerical implications. Maybe slotInitialAperture is a candidate? Let you DFN people tell what it should be.

  Note that the "dV" is less a problem because it is a difference
  (independent on the choice of the reference volume), so the
  incompressible scheme is not affected.

  Bruno

  [1]
  https://github.com/yade/trunk/blob/master/pkg/pfv/FlowEngine.ipp.in#L439

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