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August 5, 2011, 11:42 
modify laplacian: div(k*grad(a*u))

#1 
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Hello,
I am trying to solve a type of heat equation: The difference to the standard heat equation is the scalar field alpha. The problem is that the last term cannot be expressed as fvm::laplacian(k,alpha*u), because apparently alpha*u is not the right class for this argument, and the compiler fails. How can this PDE be solved? Thanks Gunnar Last edited by gunnar2; August 8, 2011 at 13:26. Reason: correction: replaced [math]\nabla\cdot\phi u[/math] with [math]\nabla\cdot\mathbf{v} u[/math] 

August 6, 2011, 05:00 

#2 
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ata kamyabi
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Hi
I think you can define a new field newfield=alpha*u and use fvc::laplacian(k,new) good luck 

August 6, 2011, 06:11 

#3 
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But I need the implicit (fvm::laplacian), not the explicit (fvc::laplacian) term.
If there is no such term, it should be possible to use something like fvm::laplacian(k,u)*diag(alpha) for . diag(alpha) would be a sparse diagonal matrix with the entries of the field alpha on it's diagonal, but I don't think such matrix exists in Openfoam. What do you think, does it make sense to implement it? Thanks Gunnar 

August 7, 2011, 05:10 

#4 
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ata kamyabi
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Hi
I do not know 

August 7, 2011, 11:42 

#5 
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Michael Roth
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How about a little chain rule? i.e. split into:
Code:
\nabla \cdot ( k \alpha \nabla u ) + \nabla \cdot ( k u \nabla \alpha ) 

August 7, 2011, 12:29 

#6 
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ata kamyabi
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Hi
But you loose conservative form. 

August 8, 2011, 08:43 

#7 
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Santiago Marquez Damian
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First of all the equation appears to be not consistent, the first and last terms are vectorial, meanwhile the second one is scalar.
Regards.
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Santiago MÁRQUEZ DAMIÁN, Ph.D. Research Scientist Research Center for Computational Methods (CIMEC)  CONICET/UNL Tel: 543424511594 Int. 7032 Colectora Ruta Nac. 168 / Paraje El Pozo (3000) Santa Fe  Argentina. http://www.cimec.org.ar 

August 21, 2011, 14:53 

#8 
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Mieszko Młody
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Hi Gunnar,
If the only think you need is modification of the discretization matrix (by multiplying diag(alpha)), then you can change the matrix itself. See the PISO algorithm from icoFoam: http://openfoamwiki.net/index.php/IcoFoam You can do similar and: 1. discretize alpha 2. UEqn.A() = UEqn.A()*alpha_discretized maybe will work... ZMM 

August 21, 2011, 16:44 

#9 
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Kai
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Kai 

August 21, 2011, 17:36 

#10 
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Mieszko Młody
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Hi Kai,
Of course, I would proceed using this transformation. Currently I have some issues with laplacian operator in OFoam as well. Could you see my post: laplacian problem Maybe you will have some suggestions... Thanks ZMM 

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