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September 1, 2013, 01:10 
How to calculate the divergence of velocity at the grid vertex

#1 
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JM
Join Date: Jul 2013
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Hello everyone
I want to calculate the divergence of velocity at the grid vertex using the value of cell center just like the attached file showing.Because the mesh file is unstructured,I don't know how to express the U(i+1,j+1)V(i+1,j+1),U(i,j+1)V(i,j+1) U(i+1,j)V(i+1,j),U(i,j)V(i,j). If anyone knows how to realize this,please tell me! Thank you very much! best regards! xiaof 

September 1, 2013, 05:51 

#2 
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Bruno Santos
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Greetings xiaof,
Have a look into:
Bruno
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September 2, 2013, 09:05 

#3 
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Philip Cardiff
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Hi xiaof,
You could calculate the cellcentred divergence field and then interpolate this volume field to the vertices, using pointVolInterpolation (available in OpenFOAM1.6ext, I'm not sure which class does this in standard OpenFOAM). Best regards, Philip 

September 2, 2013, 11:12 

#4 
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JM
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Hi Philip
Thank you for your method.With your method,I can get the divergence at the vertices.But I think it is different what I mean.I need to use the four cellcenter velocity around the vertices to get the divergence. So if I get the vertices velocity, can I use Code:
fvc::div() or fvc::grad() thank you! xiaof 

September 2, 2013, 11:32 

#5 
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Philip Cardiff
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Hi xiaof,
I am not sure I understand what exactly you want to do, but I don't think the fvc/fvm operators will do exactly what you want. The fvc/fvm operators typically deal with volume fields (cell centre) and surface fields (face centre). You might be able to active what you want by manually calculating the value for each vertex, e.g. Code:
const labelListList& pointCells = mesh.pointCells(); // go through all points forAll(mesh.points(), pointi) { // go through all cells around pointi forAll(pointCells[pointi], celli) { label cellID = pointCells[pointi][celli]; // do some calculations here, maybe using centre coordinates // e.g. divU[pointi] += mesh.C()[cellID]*U[cellID]; } } Maybe you could explain a bit more about why you need to do this calculation, then we might be able to suggest the best way. Best regards, Philip 

September 2, 2013, 20:20 

#6 
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JM
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Hi Philip
Because we want want to test a new interpolate scheme.Although the divergence at cell center approaches to zero,the divergence at cell vertices might not.So we want to calculate the divergence of velocity at the grid vertex using the value of cell center. Code:
divU[pointi] += mesh.C()[cellID]*U[cellID]; With the centre coordinates,maybe we should calculate some weight coefficient. If the mesh is not hexahedron，how to calculate it with general method? Thank you! regards! xiaof 

September 3, 2013, 10:03 

#7  
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Philip Cardiff
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Quote:
Quote:
Hi xiaof, OK that sounds like an interesting interpolation scheme. As regards this code: Code:
divU[pointi] += mesh.C()[cellID]*U[cellID]; I cannot help you figure out how to do this for an unstructured grid; however, I would suggest you start by drawing some general polygons around a vertex and see if you can figure out a general method based on surrounding cell centre velocities and coordinates I suppose. For example, OpenFOAM calculates gradients and divergences by summing up terms on each face of a cell so the method is independent of the cell shapes and number of faces. To get the cell IDs of the cells surrounding a point is easy (OpenFOAM does the work), I will rewrite part of code from my previous post with more comments: Code:
// pointCells gives you a list of the cell IDs of the cells around every mesh point const labelListList& pointCells = mesh.pointCells(); // go through all points forAll(mesh.points(), pointi) { // now we go through all cells around pointi // i.e. there are pointCells[pointi].size() cells around pointi // and pointCells[pointi] gives you a list of the cell IDs forAll(pointCells[pointi], celli) { // here is the ID of celli label cellID = pointCells[pointi][celli]; // so we can use cellID to get the velocity or coordinates below // do some calculations here, maybe using centre coordinates // just and example calculation  does not mean anything! divU[pointi] += mesh.C()[cellID]*U[cellID]; } } Philip 

September 4, 2013, 04:37 

#8 
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JM
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Hi Philip
Thank you for your explain.Now I can find the all cells around the pointi.What I want to make sue further is which one is the first one ,second one... As to the attached file,is it the leftdown cell is the first one cell.And then I can take different operation. Thank you very much! regards! xiaof 

September 4, 2013, 10:07 

#9  
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Philip Cardiff
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Quote:
In an unstructured mesh, there is no leftUp, rightUP, etc. because there might be 3 surrounding cells or 10 surrounding cells. So for your case, the only pertinent information you know is:
Philip 

December 18, 2014, 08:21 

#10 
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Niu
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Dear Philip,
I'm doing the postprocessing of a vector field, I want to take an average of velocity along one direction, but I don't know how to get the velocity at the point or center of cell. Would you mind giving me some advice? Thanks! 

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