[wilove]

I'm trying to obtain a mesh using snappyHexMesh. I'm using "consolidated" settings (in the sense that these are settings that i often use without any problem).

But in this mesh I needed to create also baffle, therefore I did only one change to the settings:

allowFreeStandingZoneFaces true;  //before was false

As far as I understood this setting may give some problem with the mesh quality. Indeed I obtained:

Layer mesh : cells:25759574  faces:80125713  points:28557646
Cells per refinement level:
    0	249533
    1	1879
    2	6680
    3	22934
    4	251389
    5	589058
    6	602221
    7	560941
    8	16150180
    9	1398684
    10	4849433
    11	301205
    12	775437
Writing mesh to time constant
Wrote mesh in = 150.001 s.
Layers added in = 14717.6 s.
Checking final mesh ...
Checking faces in error :
    non-orthogonality > 65  degrees                        : 243
    faces with face pyramid volume < 1e-013                 : 0
    faces with face-decomposition tet quality < 1e-015      : 2
    faces with concavity > 80  degrees                     : 2
    faces with skewness > 2   (internal) or 15  (boundary) : 0
    faces with interpolation weights (0..1)  < 0.05        : 0
    faces with volume ratio of neighbour cells < 0.01      : 1
    faces with face twist < 0.02                           : 0
    faces on cells with determinant < 0.001                : 0
Finished meshing with 248 illegal faces (concave, zero area or negative cell pyramid volume)
Finished meshing in = 35841.2 s.
End

But over a such a big mesh I hope they don't represent a problem.

The real problem is with BL:

Doing final balancing
---------------------

Writing 189374 added cells to cellSet addedCells
Writing 142659 faces inside added layer to faceSet layerFaces

Writing fields with layer information:
    nSurfaceLayers    : actual number of layers
    thickness         : overall layer thickness
    thicknessFraction : overall layer thickness (fraction of desired thickness)


patch         faces    layers   overall thickness
                                [m]       [%]
-----         -----    ------   ---       ---
DPE_FW        1297616  0        0         0       
DPE_Telaio    660614   0.181    0.000592  3.3     
DPE_RW        125248   0.491    0.00169   8.46    
DPE_MW        87040    0.00494  4.09e-006  0.0205  
DPE_FWheels   66032    0        0         0       
DPE_RWheels   66306    0        0         0       
DPE_Diffusore 65186    0.118    0.000225  1.25

I really don't understand what I'm doing wrong as I checked the dict many times and the mesh doesn't seem to have evident problems (exept for missing BL).

Can someone check if there are evident error in the snappyHexMeshDict I attached? Wherelse can the problem lie?

(I also uploaded here the log)

[john myce]

Hi !

Based on your SHMDict, from my point of view, to improve the layers coverage you can try to decrease the resolveFeatureAngle from the castellated phase to 15 degrees.

For the snapping phase try to activate multiRegionFeatureSnap.

And for the addLayers one, try to put nGrow to 0 because for my cases it has always produced a bad layer coverage onto the geometry.

Cheers,

[wilove]

Thank you for your suggestions!
...but my problems got worse

I increased some refinement parameter in addition to the changes you suggested. By doing so my CAD file has proved not to be watertight. Therefore I changed the STL and now it seems to be watertight.


Nevertheless snappy gets completrly stuck at the layer addition phase:

Shrinking and layer addition phase
----------------------------------

Using mesh parameters 
{
    maxNonOrtho     65;
    maxBoundarySkewness 15;
    maxInternalSkewness 2;
    maxConcave      80;
    minVol          1e-013;
    minTetQuality   1e-015;
    minArea         -1;
    minTwist        0.02;
    minDeterminant  0.001;
    minFaceWeight   0.05;
    minVolRatio     0.01;
    minTriangleTwist -1;
    nSmoothScale    4;
    errorReduction  0.75;
}


Merging all faces of a cell
---------------------------
    - which are on the same patch
    - which make an angle < 180 degrees
      (cos:-1)
    - as long as the resulting face doesn't become concave by more than 90 degrees
      (0=straight, 180=fully concave)

And then I get this error (that its pretty rare from what I see online):

--> FOAM FATAL ERROR:
Multiple outside loops:0()

    From function static Foam::face Foam::combineFaces::getOutsideFace(consPatch&)
    in file polyTopoChange/polyTopoChange/combineFaces.C at line 442.

FOAM parallel run aborting

I still managed to reconstruct the mesh of castellation and snapping phases. Everything seems really smooth and well defined.

And also with checkMesh it looks like there are no big problems:

[...]

Checking geometry...
    Overall domain bounding box (-35 -0.00524019 -4.98124e-082) (65 50 50)
    Mesh has 3 geometric (non-empty/wedge) directions (1 1 1)
    Mesh has 3 solution (non-empty) directions (1 1 1)
    Boundary openness (-1.31005e-018 4.09243e-015 -5.51466e-016) OK.
    Max cell openness = 6.28592e-016 OK.
    Max aspect ratio = 22.7249 OK.
    Minimum face area = 5.36663e-010. Maximum face area = 1.  Face area magnitudes OK.
    Min volume = 7.06024e-013. Max volume = 1.  Total volume = 250000.  Cell volumes OK.
    Mesh non-orthogonality Max: 69.4247 average: 7.13348
    Non-orthogonality check OK.
    Face pyramids OK.
 ***Max skewness = 14.538, 175 highly skew faces detected which may impair the quality of the results
  <<Writing 175 skew faces to set skewFaces
    Coupled point location match (average 0) OK.

Failed 1 mesh checks.

End

What can I do next? Since I found few online resouce on that error message I have no clue on how to adress it.

[john myce]

Hi !

Really strange,by looking at this statement :

Merging all faces of a cell
---------------------------
    - which are on the same patch
    - which make an angle < 180 degrees
      (cos:-1)
    - as long as the resulting face doesn't become concave by more than 90 degrees
      (0=straight, 180=fully concave)

I checked on some SHM log files and the angle seems pretty high as for me this angle is 30 degrees most of the time.

Merging all faces of a cell
---------------------------
    - which are on the same patch
    - which make an angle < 30 degrees (cos:0.866025403784)

I found in the fondation version code that this angle displayed (in bold) is linked to your featureAngle in the addLayers section and it is actually pretty high (250°) !



For me the limit is 180 degrees because there is no improvement above it and because it is related to other function maybe it crashes ?

so you can test with featureAngle less or equal to 180.

Cheers.

[wilove]

Thank you so much for your speedy reply!

I forgot to mention that I also had alreay lowered featureAngle at 180 deg.
In order to try your suggestion I tried to lower it further, setting it at 130 deg.

Therefore the "strange" part should now look more standard:

Merging all faces of a cell
---------------------------
    - which are on the same patch
    - which make an angle < 130 degrees
      (cos:-0.642788)
    - as long as the resulting face doesn't become concave by more than 90 degrees
      (0=straight, 180=fully concave)

But I got the same error as before.

I uploaded the full log here and the updated dict.

Do you have any further suggestion?

P.S.: Do you think this can happen because of the new STL files? I tend to exclude that since the other two phases work well... but I don't know what to think...

[john myce]

To be sure it is the STL file have you done a

checkMesh -allGeometry -allTopology

? Maybe it will help you.

I've just found this thread which is quite interesting for your error if you did not read it yet. It is talking about higher refinement level for edges or better tolerance for your CAD file.

Error snappyhexmesh - Multiple outside loops

[wilove]

Ok in these days our server is being used by someone else but I manage to run at least the checkMesh

/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  dev
     \\/     M anipulation  |

   OpenFOAM for Windows 19.04 (v1)
   Built by CFD Support, www.cfdsupport.com (based on Symscape).
\*---------------------------------------------------------------------------*/
Build  : dev-f60147f
Exec   : C:\OpenFOAM\19.10\cygwin64\opt\OpenFOAM\OpenFOAM-dev\platforms\cygwin64mingw-w64DPInt32Opt\bin\checkMesh.exe -allGeometry -allTopology
Date   : Apr 09 2020
Time   : 18:23:16
Host   : "DESKTOP-53KTC8C"
PID    : 2536
I/O    : uncollated
Case   : C:/OpenFOAM/19.10/Server Dynamis-dev/run/Mesh5
nProcs : 1
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 10)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create polyMesh for time = 0

Enabling all (cell, face, edge, point) topology checks.

Enabling all geometry checks.

Time = 0

Mesh stats
    points:           26317519
    faces:            73424513
    internal faces:   70626087
    cells:            23563099
    faces per cell:   6.1134
    boundary patches: 23
    point zones:      0
    face zones:       5
    cell zones:       2

Overall number of cells of each type:
    hexahedra:     21978955
    prisms:        320140
    wedges:        0
    pyramids:      0
    tet wedges:    753
    tetrahedra:    0
    polyhedra:     1263251
    Breakdown of polyhedra by number of faces:
        faces   number of cells
            4   107773
            5   91851
            6   246573
            7   1786
            8   1068
            9   598686
           10   260
           11   373
           12   151751
           13   14
           14   203
           15   56330
           16   3
           17   30
           18   6548
           21   2

Checking topology...
    Boundary definition OK.
    Cell to face addressing OK.
    Point usage OK.
    Upper triangular ordering OK.
    Face vertices OK.
    Topological cell zip-up check OK.
    Number of identical duplicate faces (baffle faces): 108289
  <<Number of duplicate (not baffle) faces found: 1640. This might indicate a problem.
  <<Number of faces with non-consecutive shared points: 3242. This might indicate a problem.
  <<Writing 224758 faces with non-standard edge connectivity to set edgeFaces
  <<Writing 36 cells with zero or one non-boundary face to set oneInternalFaceCells
  <<Writing 392 cells with two non-boundary faces to set twoInternalFacesCells
   *Number of regions: 37
    The mesh has multiple regions which are not connected by any face.
  <<Writing region information to "0/cellToRegion"
  <<Writing region 0 (fully disconnected) with 23563063 cells to cellSet region0
  <<Writing region 1 (fully disconnected) with 1 cells to cellSet region1
  <<Writing region 2 (fully disconnected) with 1 cells to cellSet region2
  <<Writing region 3 (fully disconnected) with 1 cells to cellSet region3
  <<Writing region 4 (fully disconnected) with 1 cells to cellSet region4
  <<Writing region 5 (fully disconnected) with 1 cells to cellSet region5
  <<Writing region 6 (fully disconnected) with 1 cells to cellSet region6
  <<Writing region 7 (fully disconnected) with 1 cells to cellSet region7
  <<Writing region 8 (fully disconnected) with 1 cells to cellSet region8
  <<Writing region 9 (fully disconnected) with 1 cells to cellSet region9
  <<Writing region 10 (fully disconnected) with 1 cells to cellSet region10
  <<Writing region 11 (fully disconnected) with 1 cells to cellSet region11
  <<Writing region 12 (fully disconnected) with 1 cells to cellSet region12
  <<Writing region 13 (fully disconnected) with 1 cells to cellSet region13
  <<Writing region 14 (fully disconnected) with 1 cells to cellSet region14
  <<Writing region 15 (fully disconnected) with 1 cells to cellSet region15
  <<Writing region 16 (fully disconnected) with 1 cells to cellSet region16
  <<Writing region 17 (fully disconnected) with 1 cells to cellSet region17
  <<Writing region 18 (fully disconnected) with 1 cells to cellSet region18
  <<Writing region 19 (fully disconnected) with 1 cells to cellSet region19
  <<Writing region 20 (fully disconnected) with 1 cells to cellSet region20
  <<Writing region 21 (fully disconnected) with 1 cells to cellSet region21
  <<Writing region 22 (fully disconnected) with 1 cells to cellSet region22
  <<Writing region 23 (fully disconnected) with 1 cells to cellSet region23
  <<Writing region 24 (fully disconnected) with 1 cells to cellSet region24
  <<Writing region 25 (fully disconnected) with 1 cells to cellSet region25
  <<Writing region 26 (fully disconnected) with 1 cells to cellSet region26
  <<Writing region 27 (fully disconnected) with 1 cells to cellSet region27
  <<Writing region 28 (fully disconnected) with 1 cells to cellSet region28
  <<Writing region 29 (fully disconnected) with 1 cells to cellSet region29
  <<Writing region 30 (fully disconnected) with 1 cells to cellSet region30
  <<Writing region 31 (fully disconnected) with 1 cells to cellSet region31
  <<Writing region 32 (fully disconnected) with 1 cells to cellSet region32
  <<Writing region 33 (fully disconnected) with 1 cells to cellSet region33
  <<Writing region 34 (fully disconnected) with 1 cells to cellSet region34
  <<Writing region 35 (fully disconnected) with 1 cells to cellSet region35
  <<Writing region 36 (fully disconnected) with 1 cells to cellSet region36

Checking patch topology for multiply connected surfaces...
                   Patch    Faces   Points                  Surface topology Bounding box
                    side     5000     5151  ok (non-closed singly connected) (-35 50 -2.30247e-082) (65 50 50)
                symmetry   101167   105508  ok (non-closed singly connected) (-35 0 0) (65 0 50)
                   inlet     2500     2601  ok (non-closed singly connected) (-35 0 -2.30247e-082) (-35 50 50)
                  outlet     2500     2601  ok (non-closed singly connected) (65 0 -2.01398e-205) (65 50 50)
                  ground   168036   170148  ok (non-closed singly connected) (-35 0 -2.30247e-082) (65 50 1.63036e-096)
                     top     5000     5151  ok (non-closed singly connected) (-35 0 50) (65 50 50)
                  DPE_FW  1309273  1371181  ok (non-closed singly connected) (-0.935107 0 0.0580856) (-0.159418 0.738514 0.351191)
               Radiatori        0        0                        ok (empty)
         Radiatori_slave        0        0                        ok (empty)
                Batterie        0        0                        ok (empty)
          Batterie_slave        0        0                        ok (empty)
              DPE_Telaio   332613   359471  ok (non-closed singly connected) (-0.890818 -0.000595452 0.0276807) (1.98007 0.424718 1.15159)
                  DPE_RW   125824   128733  ok (non-closed singly connected) (1.31592 0 0.514995) (2.03688 0.497021 1.18858)
                  DPE_MW    87578    90895  ok (non-closed singly connected) (0.149646 0.242772 0.0322572) (1.44492 0.697 0.255685)
             DPE_FWheels   186044   204028  ok (non-closed singly connected) (-0.237524 0.435268 0) (0.237291 0.70396 0.470094)
             DPE_RWheels   186046   204078  ok (non-closed singly connected) (1.31248 0.435267 0) (1.78729 0.70396 0.470084)
           DPE_Diffusore    65037    67700  ok (non-closed singly connected) (-0.00282152 0 0.0272791) (2.0339 0.696113 0.258254)
            Fan_Batterie    77990    82645  ok (non-closed singly connected) (1.89678 0.0868613 0.240428) (1.97834 0.176631 0.287517)
      Fan_Batterie_slave    79319    82678  ok (non-closed singly connected) (1.89678 0.0868613 0.240428) (1.97834 0.176631 0.287517)
    Fan_Batterie_Centrale     7519     8427  ok (non-closed singly connected) (1.89678 0 0.250428) (1.97834 0.0484366 0.297517)
    Fan_Batterie_Centrale_slave     7519     8427  ok (non-closed singly connected) (1.89678 0 0.250428) (1.97834 0.0484366 0.297517)
           Fan_Radiatori    24492    28238  ok (non-closed singly connected) (1.51297 0.0416183 0.295898) (1.54402 0.13241 0.381188)
     Fan_Radiatori_slave    24969    28298  ok (non-closed singly connected) (1.51297 0.0416183 0.295898) (1.54402 0.13241 0.381188)

Checking geometry...
    Overall domain bounding box (-35 -0.000595452 -2.30247e-082) (65 50 50)
    Mesh has 3 geometric (non-empty/wedge) directions (1 1 1)
    Mesh has 3 solution (non-empty) directions (1 1 1)
    Boundary openness (3.25169e-020 3.11938e-015 -2.22712e-016) OK.
    Max cell openness = 4.43716e-016 OK.
    Max aspect ratio = 15.6226 OK.
    Minimum face area = 1.31544e-010. Maximum face area = 1.  Face area magnitudes OK.
    Min volume = 6.15459e-013. Max volume = 1.  Total volume = 250000.  Cell volumes OK.
    Mesh non-orthogonality Max: 68.5929 average: 7.11855
    Non-orthogonality check OK.
    Face pyramids OK.
 ***Max skewness = 14.8851, 343 highly skew faces detected which may impair the quality of the results
  <<Writing 343 skew faces to set skewFaces
    Coupled point location match (average 0) OK.
 ***Error in face tets: 6 faces with low quality or negative volume decomposition tets.
  <<Writing 6 faces with low quality or negative volume decomposition tets to set lowQualityTetFaces
   *Edges too small, min/max edge length = 4.16334e-017 1, number too small: 122922
  <<Writing 122922 points on short edges to set shortEdges
  <<Writing 122929 near (closer than 0.000122475 apart) points to set nearPoints
   *There are 27647 faces with concave angles between consecutive edges. Max concave angle = 79.9829 degrees.
  <<Writing 27647 faces with concave angles to set concaveFaces
    Face flatness (1 = flat, 0 = butterfly) : min = 0.24589  average = 0.999661
   *There are 842 faces with ratio between projected and actual area < 0.8
    Minimum ratio (minimum flatness, maximum warpage) = 0.24589
  <<Writing 842 warped faces to set warpedFaces
    Cell determinant (wellposedness) : minimum: 0 average: 11.1708
 ***Cells with small determinant (< 0.001) found, number of cells: 659
  <<Writing 659 under-determined cells to set underdeterminedCells
 ***Concave cells (using face planes) found, number of cells: 575706
  <<Writing 575706 concave cells to set concaveCells
    Face interpolation weight : minimum: 0.0502973 average: 0.484304
    Face interpolation weight check OK.
    Face volume ratio : minimum: 0.0101874 average: 0.919812
    Face volume ratio check OK.

Failed 4 mesh checks.

End

I see big problems but I really don't know what can be the cause of such a bad quality, given the high settings I'm using.


Regarding the topic you linked me: I've already read it, I tried to increase some parameter but, as you can see from the dict, they are already pretty high (therefore I'm already at the limit of server resources).
Should I try to increase some setting even further or do you suggest something else?

[john myce]

To be honest I'm running out of ideas.
Maybe changing the decomposition method or drastically the version of OpenFOAM could solve this kind of problem.

[wilove]

To be honest I'm running out of ideas.

Anyway, thanks for your help!

I'm posting a quick update if someone wants to share any other idea.
This is what I've done so far:

1. Imported my STL files in a website in order to fix them. This was certanly a good step forward because the resulting files were "approved" by surfaceCheck
2. I tried to mesh something with my personal PC (using the same STL files but obviously with lowered refinement settings and just 1 boundary layer). Everything worked smoothly despite the low quality of the mesh.
3. Up until now I used on the server an OpenFOAM version compiled for Windows whereas my PC runs Ubuntu. Therefore I thought that the problem lied there and I managed to start meshing on a Ubuntu server.
   Nevertheless, using high refinement settings, I obtain the same error also on this system. The only difference is that now the error is better described (but still unintelligible):
   

   [9] 
   [9] 
   [9] --> FOAM FATAL ERROR: 
   [9] [9]     in file polyTopoChange/polyTopoChange/combineFaces.C at line 419.
   [9] 
   FOAM parallel run aborting
   [9] 
   [9] #0  Foam::error::printStack(Foam::Ostream&) at ??:?
   [9] #1  Foam::error::abort() at ??:?
   [9] #2  Foam::combineFaces::getOutsideFace(Foam::PrimitivePatch<Foam::face, Foam::IndirectList, Foam::Field<Foam::Vector<double> > const&, Foam::Vector<double> > const&)[10] 
   [10] 
   [10] --> FOAM FATAL ERROR: 
   [10] Multiple outside loops:0()
   [10] 
   [10]     From function static Foam::face Foam::combineFaces::getOutsideFace(const indirectPrimitivePatch&)
   [10]     in file polyTopoChange/polyTopoChange/combineFaces.C at line 419.
   [10] 
   FOAM parallel run aborting
   [10] 
   [10] #0  Foam::error::printStack(Foam::Ostream&) at ??:?
   [10] #1  Foam::error::abort() at ??:?
   [10] #2  Foam::combineFaces::getOutsideFace(Foam::PrimitivePatch<Foam::face, Foam::IndirectList, Foam::Field<Foam::Vector<double> > const&, Foam::Vector<double> > const&) at ??:?
   [9] #3  Foam::combineFaces::validFace(double, Foam::PrimitivePatch<Foam::face, Foam::IndirectList, Foam::Field<Foam::Vector<double> > const&, Foam::Vector<double> > const&) at ??:?
   [10] #3  Foam::combineFaces::validFace(double, Foam::PrimitivePatch<Foam::face, Foam::IndirectList, Foam::Field<Foam::Vector<double> > const&, Foam::Vector<double> > const&) at ??:?
   [9] #4  Foam::combineFaces::getMergeSets(double, double, Foam::HashSet<int, Foam::Hash<int> > const&) const at ??:?
   [10] #4  Foam::combineFaces::getMergeSets(double, double, Foam::HashSet<int, Foam::Hash<int> > const&) const at ??:?
   [9] #5  Foam::meshRefinement::mergePatchFacesUndo(double, double, Foam::List<int> const&, Foam::dictionary const&, Foam::List<int> const&) at ??:?
   [10] #5  Foam::meshRefinement::mergePatchFacesUndo(double, double, Foam::List<int> const&, Foam::dictionary const&, Foam::List<int> const&) at ??:?
   [9] #6  Foam::snappyLayerDriver::mergePatchFacesUndo(Foam::layerParameters const&, Foam::dictionary const&) at ??:?
   [10] #6  Foam::snappyLayerDriver::mergePatchFacesUndo(Foam::layerParameters const&, Foam::dictionary const&) at ??:?
   [10] #7  Foam::snappyLayerDriver::doLayers(Foam::dictionary const&, Foam::dictionary const&, Foam::layerParameters const&, bool, Foam::decompositionMethod&, Foam::fvMeshDistribute&) at ??:?
   [9] #7  Foam::snappyLayerDriver::doLayers(Foam::dictionary const&, Foam::dictionary const&, Foam::layerParameters const&, bool, Foam::decompositionMethod&, Foam::fvMeshDistribute&) at ??:?
   [10] #8   at ??:?
   [9] #8  ?? in "/opt/openfoam6/platforms/linux64GccDPInt32Opt/bin/snappyHexMesh"
   [10] #9  __libc_start_main in "/opt/openfoam6/platforms/linux64GccDPInt32Opt/bin/snappyHexMesh"
   [9] #9  __libc_start_main in "/lib/x86_64-linux-gnu/libc.so.6"
   [10] #10   in "/lib/x86_64-linux-gnu/libc.so.6"
   [9] #10  ? in "/opt/openfoam6/platforms/linux64GccDPInt32Opt/bin/snappyHexMesh"

Maybe changing the decomposition method or drastically the version of OpenFOAM could solve this kind of problem

Therefore changing the version of OF does not help, but I will try changing the decomposition method.


Just a final considerations after reading this comment (and in general the whole topic):
I think that there is nothing wrong in my STL files nor in my snappyHex settings per se, but probably the combination of both, at high refinements, generates that problem.

Unfortunately I cannot share my geometry but I hope that someone has some suggestions on how to avoid that behavior in general.

[wilove]

I think I managed to solve my problem. There were mainly 3 problems:

1. I didn't compute accurately the last layer dimension in comparison with the cell dimension. This was one the causes of the bad bl addition.
   My suggestion for everyone that will read this post is to perform only the snapping and castellation phases. Check the meshes and check accurately if the last bl thickness is smaller than the local cell dimension.
2. The multi-region mesh that I obtained was the cause of the Multiple outside loops:0() error. Running the splitMeshRegions command solved this but the quality of the mesh was still bad.
3. The thing that improved the quality of the mesh (in particular the multiple regions were not created anymore) is the modification of my geometry at the symmetry-plane.

In addition, I set an higher number of iterations both for the snapping and the layer addition phases. And this made checkMesh a little happier.

Just a note about this:

I found in the fondation version code that this angle displayed (in bold) is linked to your featureAngle in the addLayers section and it is actually pretty high (250°)!
For me the limit is 180 degrees because there is no improvement above it and because it is related to other function maybe it crashes?
so you can test with featureAngle less or equal to 180.

While trying to solve my problem, I found out this PDF where the following was reported:

According to own tests, in contrast to φrfA also values of φfA above 180° do influence the result, therefore maximum value 360° is set.

I really don't know who is right since I don't have time to test. But still, I thought it was worthy to report this to you and to the readers of the thread.

Anyway, thank you again for your help!

[john myce]

I'm glad you've solved your problem !

Thanks for sharing this interesting paper.