# Solving coupled equations in one domain

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 February 16, 2012, 10:31 Solving coupled equations in one domain #1 New Member   Jonas Due Vesterheden Join Date: Oct 2011 Posts: 2 Rep Power: 0 Hello, I need to solve a steady state problem for two scalar fields on the same domain. The governing equations are: a and b are coupled by the bounday conditions: Where n is the outward surface normal. I have tried creating a solver that simply uses Code: ```solve(fvm::laplacian(a) + k*k*a); solve(fvm::laplacian(b) + k*k*b);``` and using groovyBC for the boundary conditions, but this of course does not work since the coupling is not taken into consideration. What would be the best approach for solving these equations? I have found coupledFvScalarMatrix in openfoam-extend, would that be applicable to my problem? Are there any other methods I could try? Best regards, Jonas

 February 17, 2012, 13:51 #2 Super Moderator     Philip Cardiff Join Date: Mar 2009 Location: Dublin, Ireland Posts: 1,089 Rep Power: 34 Jonas, You could look at solidDisplacementFoam which solves for T and D (on the same mesh), where there is one way coupling. Or you could look at icoFsiFoam which solves for U and D (on different meshes), where there is two way coupling. Essentially both of these solve the equations like you did except they have an outer correction loop allowing the whole system to converge. Also you might need to relax your 'a' and 'b' after solving to achieve better convergence. Philip

 April 2, 2012, 11:10 #3 New Member   Gilles De Neyer Join Date: Nov 2011 Posts: 18 Rep Power: 14 I post in this topic as I think I have to use the coupledMatrix : I would like to solve to different set of equation in two parts of my domain: and a the interface I would like to impose U_left = U_right p_left = p_right and then classics inlet/outlet condition for the entire domain. I have checked the cases for Fluid-Structure interaction but it's not useful for my case. I don't know how I can impose a boundary condition taking into account the solution of the other problem at each time step :-s If someone got a solution I would be really glad to hear it

 April 2, 2012, 12:24 #4 Senior Member     Hisham Elsafti Join Date: Apr 2011 Location: Braunschweig, Germany Posts: 257 Blog Entries: 10 Rep Power: 17 Hi You may need to loop the solution of your equations while updating coefficients for your BCs. Have a look at the SIMPLE algorithm: http://openfoamwiki.net/index.php/Th...hm_in_OpenFOAM Best regards, Hisham El Safti

 April 2, 2012, 13:30 #5 New Member   Gilles De Neyer Join Date: Nov 2011 Posts: 18 Rep Power: 14 Thanks you for your answer Hisham I'm not sure I got this, you mean : solving for U_left ; impose U_right.boundaryfield[patchlabel] = U_left.boundaryfield[patchlabel]; solving for U_right; U_left.correctboundarycondition; U_right.correctboundarycondition; My problem is that using the correctboundarycondition will give me bad answer anyway as there is no condition to say "the inlet velocity is the same as the outlet velocity from domain 1 which has been calculated with nodes of domain 1 AND domain2) Is my point understandable ? :-) it's quite hard to explain in a few words ...

April 2, 2012, 14:01
#6
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Hisham Elsafti
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Hi gdeneyer,

Take a look at the cyclic boundary condition. It is supposed to reduce repetitive geometries by imposing similar continuity conditions on two separate patches. Nevertheless, I am not sure whether it would work for your case!

If your first domain solves and passes values (in a one-way fashion) to the other domain, then why not do the simulations of both domains separately?

Another idea would be to treat both domains in the same fashion as porous media in OF so you would not need any additional work at the two domains interface (they would actually be one domain with extra terms in the PDEs turned on for one domain and off for the other).

Best regards,
Hisham El Safti

Quote:
 Originally Posted by gdeneyer Thanks you for your answer Hisham I'm not sure I got this, you mean : solving for U_left ; impose U_right.boundaryfield[patchlabel] = U_left.boundaryfield[patchlabel]; solving for U_right; U_left.correctboundarycondition; U_right.correctboundarycondition; My problem is that using the correctboundarycondition will give me bad answer anyway as there is no condition to say "the inlet velocity is the same as the outlet velocity from domain 1 which has been calculated with nodes of domain 1 AND domain2) Is my point understandable ? :-) it's quite hard to explain in a few words ...

April 2, 2012, 14:29
#7
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Gilles De Neyer
Join Date: Nov 2011
Posts: 18
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Quote:
 Originally Posted by Hisham Another idea would be to treat both domains in the same fashion as porous media in OF so you would not need any additional work at the two domains interface (they would actually be one domain with extra terms in the PDEs turned on for one domain and off for the other).
Well, it seems to me that it would be exactly what I'm looking for, I'm gonna look into that direction.

Thanks you for your help !