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February 28, 2012, 11:51 
Meaning of "fvc::div(phi)"

#1 
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Jeong Kim
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Hi Foamers,
When I look at pEqn.C in the "twoPhaseEulerFoam" solver, I don't really understand the following codes. ....... for(int nonOrth=0; nonOrth<=nNonOrthCorr; nonOrth++) { fvScalarMatrix pEqn ( fvm::laplacian(Dp, p) == fvc::div(phi) ); ..... Speaking of div(phi), divergence of any scalar is zero mathematically. Divergence reduce the order rank of maxtrix. For an example, let's say, velcotiy vector u=(ux, uy) div(u)=ux/dx + uy/dy > scalar quantity But, scalar phi=phi(x,y) div(phi)=0 So what is the meaning of div(phi) and what's a mathematical formulation for the term in openfoam? 

July 16, 2013, 04:01 

#2 
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Dongyue Li
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Hi Kim,
This problem happens to me in the same time!icoFoam's pressure possion equation. Did you find a solution? 

July 16, 2013, 06:01 

#3 
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Felipe Portela
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Isn't phi simply the mass flux rho*U*A ? check this
HTML Code:
http://openfoamwiki.net/index.php/Uguide_table_of_fields HTML Code:
http://openfoamwiki.net/index.php/Main_FAQ#What_is_the_field_phi_that_the_solver_is_writing Cheers, Felipe 

July 16, 2013, 08:31 

#4 
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July 16, 2013, 08:35 

#5 
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Bernhard
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No, because U is the cell centre value, and the divergence is obtained from the face values, i.e. phi.


July 16, 2013, 08:38 

#6 
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Dongyue Li
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Hi Bernhard,
Could you explain more? 

July 16, 2013, 08:39 

#7 
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Bernhard
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Can you be more specific?


July 16, 2013, 08:44 

#8 
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Dongyue Li
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July 16, 2013, 08:49 

#9 
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Bernhard
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The book are correct, but is valid without a mesh. If you integrate this equation over a control volume, this converts to a summation over the faces of the velocity times the area ( http://en.wikipedia.org/wiki/Divergence_theorem ). phi is nothing less then the velocity at the face (times the density and the face area).


July 16, 2013, 08:51 

#10 
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Felipe Portela
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July 16, 2013, 09:24 

#11  
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Dongyue Li
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Quote:
I know this, but phi is a scalar, what is div(scalar)..... Felipe. Yeah, you are right~ 

July 16, 2013, 09:27 

#12 
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Bernhard
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July 16, 2013, 09:56 

#13 
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Dongyue Li
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July 16, 2013, 10:01 

#14 
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Bernhard
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You apply the divergence theorem.
You can't integrate face values over a volume as you are posting. The difference between a volScalarField and a surfaceScalarField, is that for a volScalarField, there is a value stored per control volume or cell. For a surfaceScalarField there is a value stored per face. You can of course interpolate from the one to the other, but this is only accurate to some order. 

July 16, 2013, 10:23 

#15 
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Dongyue Li
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Quote:
Does it mean fvc::div(phi)=0 equals to sum(phi)=0 in OpenFOAM? Why doesnt it use sum(phi)=0 instead. At last,I think I need to clear my head. Thanks for you patience. Really thankful. 

July 17, 2013, 23:52 

#16 
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Dongyue Li
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Im still confused!!!!!!
div(u)=0 I know its meaning. 1) If via continuity, we have div(phi)=0, then we make an intergration on this equation like this: [LaTeX Error: Syntax error] Is this weird? 

July 18, 2013, 01:59 

#17 
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Bernhard
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Yes, this is extremely weird. phi only lives in the discretized domain on faces of cells. The is no way you can do a volume integral over such a variable.
Do you know how to derive the equation ? You can do this using a massmicrobalanse. This has not yet anything to do with a mesh, but if you understand this, it is easily translated. 

July 18, 2013, 18:46 

#18 
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Dongyue Li
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Quote:
Code:
fvScalarMatrix pEqn ( fvm::laplacian(rAU, p) == SUM(phiHbyA)//If there existed "SUM" ); Anyway thanks bro. BTW, the unit of fvc::div(u) and fvc::div(phi) is the same: Code:
fvc::div(HbyA):dimensions [0 0 1 0 0 0 0]; internalField nonuniform List<scalar> 9(0.157469 0.0674757 0.487085 0.960691 0.789192 0.715649 30.1762 0.258981 30.5822); fvc::div(phiHbyA):dimensions [0 0 1 0 0 0 0]; internalField nonuniform List<scalar> 9(0.435688 0.0982547 0.152804 0.0448476 0.720155 0.152663 28.2072 0.236062 28.5848); 

July 22, 2013, 04:01 

#19 
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Artem Shaklein
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Take into account that mathematical and OpenFOAM's languages are different.
Originally, mathematical divergence is vector operation that gives you source or sink at a point. When you use finite volume method to discretize differential equation, you get linear form of diff. equation and volumes to store discrete variables. That's why in order to get divergence you should firstly compute fluxes at volume faces. In OF there are two ways to compute divergence: 1) take fvc::div( of volVectorField ). You can see in sources, it calls for fvc::surfaceIntegrate ( volVectorField & mesh.Sf() ). 2) make first step manually (i.e. phi = U&mesh.Sf()) and call for fvc::div( surfaceScalarField phi ). Again, OF will make fvc::surfaceIntegrate ( surfaceScalarField ). Mathematically div(scalar phi) has no sense. Because you think of variables as continuous fields, but in OF variables are discrete fields. You are partially right, there is no "SUM", but "surfaceIntegrate" called by OF to compute div. And again, phi = U & mesh.Sf(). div(phi) = div(U) = div(U&mesh.Sf()). That's why you get same dimensions. 

August 23, 2013, 00:08 

#20  
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Dongyue Li
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Quote:
1. volVectorField U; fvc::div(U); 2. volVectorField U; phi = U & mesh.Sf(); fvc::div(phi); So these two functions are the same rite? fvc::div(u)=fvc::div(phi). Looks like div() has been overloaded. I make a testify: Code:
fvc::div(HbyA)dimensions [0 0 1 0 0 0 0]; internalField nonuniform List<scalar> 9(0.000569046 8.589e06 0.000648869 0.00128281 0.000183935 0.00124553 0.00416702 3.71583e06 0.00422898); fvc::div(phiHbyA):dimensions [0 0 1 0 0 0 0]; internalField nonuniform List<scalar> 9(0.000569046 8.589e06 0.000648869 0.00128281 0.000183935 0.00124553 0.00416702 3.71583e06 0.00422898); Last edited by sharonyue; August 23, 2013 at 03:35. 

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