# Cell determinant (wellposedness)

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 September 27, 2010, 14:04 Cell determinant (wellposedness) #1 New Member   Oscar Join Date: Jun 2009 Location: Murcia, Spain Posts: 14 Rep Power: 15 I'm pretty sure there isn't a single thread in the forum dealing with this thema and I hope that somebody can shed some light on this. checkMesh says my mesh is OK, but if I run "checkMesh -allGeometry -allTopology" I get a huge number of cells with small determinant that are written to a faceSet undeterminedCells. I guess I need to change my numerical schemes, but in order to do that I need to understand how this small determinant values affect my simulations. Can anybody please comment on that? Thanks! PS.- I know I could re-build the mesh and get rid of the low determinants, but this is not the point. I would like to understand their effect on the numerics. amuzeshi likes this.

 April 5, 2011, 05:23 #2 Senior Member   Andrea Ferrari Join Date: Dec 2010 Posts: 319 Rep Power: 15 I have the same problem. Did you find any solution? andrea

 August 30, 2011, 09:40 #3 Member   Join Date: Nov 2009 Location: Germany Posts: 96 Rep Power: 15 I'm also interested in this. Has anyone some experience with this issue? Does this even effect the simulation? __________________ "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." Werner Heisenberg

 April 17, 2012, 13:26 #4 Member   ms Join Date: Mar 2009 Location: West London Posts: 47 Rep Power: 15 I'm interested too and can't find anywhere on this site that helps! and then...... I realised the cells in question were extruded triangles; the extrusion resulted in all nodes of the wedges being in contact with a boundary condition: symmetry on one side, no slip on the other two: all nodes in each wedge are on a defined boundary. Perhaps that's the issue. They don't seem to be affecting solution too much. holodeck10 likes this.

 November 25, 2019, 09:25 #5 Senior Member   chandra shekhar pant Join Date: Oct 2010 Posts: 216 Rep Power: 15 Dear All, I am also facing the same issue, with "checkMesh" every thing is perfect and it says "Mesh OK". But with the "checkMesh -allTopology -allGeometry", it is showing "Failed 1 mesh checks" because of ***Cells with small determinant (< 0.001) found, number of cells: 210. (I assume). Andsince my results are not converging for SIMPLE and for PIMPLE or/and interphasechangefoam they are crashing after a while (and if not crashing then they are stuck at a point). I doubt that I will be able to make a better mesh. Does any one has found some thing in this context. If yes then please share, it will be a great help. Thanks a lot!

 April 20, 2021, 21:32 #6 Senior Member   Claudio Boezio Join Date: May 2020 Location: Europe Posts: 137 Rep Power: 5 To my surprise, I've noticed the same thing today as well. Especially interesting because I ran checkMesh -allGeometry on a case that I know to converge very well and it exhibits the same error. I took a look at the cells by running foamToVTK -cellSet underdeterminedCells and opening them with ParaView. The mesh is purely hexahedral and the only thing remarkable about those cells is that they are flat, i.e. at least one group of edges is considerably longer than the other two. According to meshQualityDict: Code: ```//- Minimum normalised cell determinant. This is the determinant of all // the areas of internal faces. It is a measure of how much of the // outside area of the cell is to other cells. The idea is that if all // outside faces of the cell are 'floating' (zeroGradient) the // 'fixedness' of the cell is determined by the area of the internal faces. // 1 = hex, <= 0 = folded or flattened illegal cell minDeterminant 0.001;``` I don't understand this description and what it means for the numerical solution. It could be the Jacobian Determinant, according to this source at page 39, but I'm not sure. ghastbug likes this.

February 8, 2022, 12:51
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I found this formula (attached image) on a snappyHexMesh pdf by Enggys, data at the bottom.

I don't understant what it means yet, but, it looks like A is the sum of the cell's areas, Ai is each face area, and tij is weird. I'm bad with component notation.

Edit: I made a 20x20x1 m plate in blockMesh, with 20x20x1 cells, and displayed the determinants on paraview. You can find it as an attached image. It looks like cell determinants depend on how many of the cell's faces touch boundaries, as opposed to how many cell faces are internal, and thus touch other cells. But I have no way to confirm it

Quote:
 (A Comprehensive Tour of snappyHexMesh 7th OpenFOAM Workshop 25 June 2012)
Attached Images
 determinant.png (96.3 KB, 43 views) determinantfoto.png (98.2 KB, 37 views)

Last edited by ghastbug; February 9, 2022 at 04:19. Reason: new info

 Tags determinant, mesh, pressure, quality, scheme

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