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 August 5, 2011, 11:42 modify laplacian: div(k*grad(a*u)) #1 New Member   Join Date: Aug 2011 Posts: 6 Rep Power: 7 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 $\nabla\cdot\phi u$ with $\nabla\cdot\mathbf{v} u$

 August 6, 2011, 05:00 #2 Senior Member     ata kamyabi Join Date: Aug 2009 Location: Kerman Posts: 322 Rep Power: 10 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 New Member   Join Date: Aug 2011 Posts: 6 Rep Power: 7 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 Senior Member     ata kamyabi Join Date: Aug 2009 Location: Kerman Posts: 322 Rep Power: 10 Hi I do not know

 August 7, 2011, 11:42 #5 Member   Michael Roth Join Date: Mar 2009 Location: Guelph, Ontario, Canada Posts: 46 Rep Power: 9 How about a little chain rule? i.e. split into: Code: \nabla \cdot ( k \alpha \nabla u ) + \nabla \cdot ( k u \nabla \alpha ) Then treat the first term implicit (by defining a new diffusivity of k\alpha) and second term explicit.

 August 7, 2011, 12:29 #6 Senior Member     ata kamyabi Join Date: Aug 2009 Location: Kerman Posts: 322 Rep Power: 10 Hi But you loose conservative form.

 August 8, 2011, 08:43 #7 Senior Member     Santiago Marquez Damian Join Date: Aug 2009 Location: Santa Fe, Santa Fe, Argentina Posts: 430 Rep Power: 16 First of all the equation appears to be not consistent, the first and last terms are vectorial, meanwhile the second one is scalar. Regards. __________________ Santiago MÁRQUEZ DAMIÁN, Ph.D. Research Scientist Research Center for Computational Methods (CIMEC) - CONICET/UNL Tel: 54-342-4511594 Int. 7032 Colectora Ruta Nac. 168 / Paraje El Pozo (3000) Santa Fe - Argentina. http://www.cimec.org.ar

 August 21, 2011, 14:53 #8 Senior Member   Mieszko Młody Join Date: Mar 2009 Location: POLAND, USA Posts: 136 Rep Power: 9 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 Member   Kai Join Date: May 2010 Location: Stockholm Posts: 45 Blog Entries: 1 Rep Power: 8 __________________ Kai

 August 21, 2011, 17:36 #10 Senior Member   Mieszko Młody Join Date: Mar 2009 Location: POLAND, USA Posts: 136 Rep Power: 9 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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