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July 10, 2013, 09:28 |
Add a constraint equation
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#1 |
New Member
sébastien cadalen
Join Date: Jul 2013
Posts: 1
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Dear all,
This post is about the way to impose an integral relation on the problem variables. As an example, let us consider a steady-state thermal transport problem with the following constraint: where is the fluid domain, is the volume of the fluid domain, and a given temperature. From a mathematical point of view this is equivalent to introduce a constant source term in the domain to satisfy the constraint. If the unconstrain problem is writen in the discrete space hence the constrained problem is: where is a row vector composed of (the cell volume divided by the total volume) and is the Lagrange multiplier associated to the constraint. This way the constraint is implicitly solved. We can also imagine the same kind of contraint on a part of the domain, on a surface of the domain, or involving more than one unknown, etc. Is there any way to solve such a problem with implicit or explicit method? If yes, how behaves the linear solvers with such a matrix to invert? Best regards, Sébastien |
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April 2, 2019, 15:23 |
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#2 |
Member
Join Date: Feb 2018
Posts: 91
Rep Power: 8 |
Hello,
Were you able to figure out the solution to a problem. I am trying to add a constraint equation in OpenFOAM |
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September 21, 2021, 07:26 |
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#3 |
New Member
Join Date: Feb 2016
Posts: 13
Rep Power: 10 |
Hi all,
I would also want to impose a constraint as an integral relation over the whole fluid domain, but I do not know how to to do it.. Do you have some ideas ? May I use " fvOptions type vectorDomainIntegral; " ? How it works ? Is there somewhere any tutorial ? Thank you Fanny PS: I am using OpenFOAM v7. |
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