CFD Online URL
[Sponsors]
Home > Forums > OpenFOAM

Reference on the Lack of Uniqueness of the Cell Volume

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   December 19, 2012, 09:58
Default Reference on the Lack of Uniqueness of the Cell Volume
  #1
ngj
Senior Member
 
Niels Gjoel Jacobsen
Join Date: Mar 2009
Location: Rotterdam, The Netherlands
Posts: 1,552
Rep Power: 23
ngj will become famous soon enoughngj will become famous soon enough
Good afternoon to all of you,

I have for a while been looking for a reference, which discuss the volume of a general hexahedral cell, i.e. non-planar faces.

I have found some references which hint that the volume of such a hexahedral cell is not uniquely defined, and based on some practical tests with different methods to compute the volume, I have reached the same conclusion.

Nonetheless, I would be grateful if anyone of you know about an article, which directly addresses the non-uniqueness in evaluating the volume of a general hexahedral cell.

Thank you and Merry Christmas,

Niels
ngj is offline   Reply With Quote

Old   December 19, 2012, 14:03
Default
  #2
Senior Member
 
Sandeep Menon
Join Date: Mar 2009
Location: Amherst, MA
Posts: 370
Rep Power: 14
deepsterblue will become famous soon enough
Why just hexahedral cells? Any general (non-simplical) polyhedral cell with non-planar faces would apply.
It depends on how you decompose the cell during the calculation. I've seen that a face-and-cell decomposition gives the best results.
__________________
Sandeep Menon
University of Massachusetts Amherst
https://github.com/smenon
deepsterblue is offline   Reply With Quote

Old   December 19, 2012, 14:14
Default
  #3
Senior Member
 
kmooney's Avatar
 
Kyle Mooney
Join Date: Jul 2009
Location: Amherst, MA USA - San Diego, CA USA
Posts: 252
Rep Power: 8
kmooney is on a distinguished road
If every face is decomposed consistently, I believe the errors in volume will at least cancel out globally.
kmooney is offline   Reply With Quote

Old   December 19, 2012, 18:09
Default
  #4
ngj
Senior Member
 
Niels Gjoel Jacobsen
Join Date: Mar 2009
Location: Rotterdam, The Netherlands
Posts: 1,552
Rep Power: 23
ngj will become famous soon enoughngj will become famous soon enough
Good evening,

Thanks for your replies.

Right now I am working on an article, where I have found myself in the need to compute the volume of a general hexahedral in order to prove a conservation property, however, since the volume appears to be non-uniquely defined, I find myself unable to give a full proof. Therefore, I would like to be able to refer to a firm/non-arguable statement/proof/article that the volume is indeed non-unique.

Kind regards,

Niels
ngj is offline   Reply With Quote

Old   December 19, 2012, 20:05
Default
  #5
Senior Member
 
kmooney's Avatar
 
Kyle Mooney
Join Date: Jul 2009
Location: Amherst, MA USA - San Diego, CA USA
Posts: 252
Rep Power: 8
kmooney is on a distinguished road
Hi Niels,

This paper:
http://citeseerx.ist.psu.edu/viewdoc...0.1.1.226.4098
mentions that without an expression for the surface that comprises a non-planar face, there is no information available to define it (pg. 5) and you need to make something up and approximate before decomposition. The fact that you need to base your decomposition on some approximation, and volume is a function of that decomposition, tell me that it is not unique.


This paper (sec. 4.2):
http://dl.acm.org/citation.cfm?id=614335

Mentions that you need to be consistent in decomposition. Since you have different options when decomposing a polyhedra, I'm thinking this implies that you can get different volume calculations.

If you search around for "tetrahedral subdivisions" or words like that you should find some more useful info. Sorry I can't give you a concrete answer on this.

Cheers!

Kyle
kmooney is offline   Reply With Quote

Old   December 20, 2012, 05:24
Default
  #6
ngj
Senior Member
 
Niels Gjoel Jacobsen
Join Date: Mar 2009
Location: Rotterdam, The Netherlands
Posts: 1,552
Rep Power: 23
ngj will become famous soon enoughngj will become famous soon enough
Hi Kyle,

Thank you, I think those references should do the trick - at least they lend sufficient support to my arguments

Merry Christmas,

Niels
ngj is offline   Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
OF211: ThirdParty and /src compiled, but not /applications... vkrastev OpenFOAM Installation 8 October 18, 2012 16:53
mesh airfoil NACA0012 anand_30 OpenFOAM Meshing & Mesh Conversion 12 December 12, 2011 05:16
Constant velocity of the material Sas CFX 15 July 13, 2010 09:56
Axisymmetrical mesh Rasmus Gjesing (Gjesing) OpenFOAM Native Meshers: blockMesh 10 April 2, 2007 15:00
Building OpenFoAm on SGI Altix 64bits anne OpenFOAM Installation 8 June 15, 2006 10:27


All times are GMT -4. The time now is 10:31.