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 February 16, 2011, 09:28 Adjoint method #1 New Member   Join Date: Jul 2009 Posts: 10 Rep Power: 10 Hi, Is there anybody who have experiences with the adjoint method to optimise a geometry? I implemented the adjoint equations based on papers and work of C. Othmers: ================================================= tmp adUEqn ( ... ); ================================================= I think my problem is in the pressure correction. In all papers that i found they use the simple method and i did it in the same way: ================================================= adp.boundaryField().updateCoeffs(); ... for (int nonOrth=0; nonOrth<=nNonOrthCorr; nonOrth++) { fvScalarMatrix adpEqn ( ... ); ================================================= If I calculated adU there are values with 10^(11) or sometimes 10^(30) near the outlet-patch. I think that is not correct Thanks for every comment. Regards, Jens Last edited by Jens; March 14, 2011 at 12:39.

 February 17, 2011, 03:50 #2 Senior Member   Karl-Johan Nogenmyr Join Date: Mar 2009 Location: Linköping Posts: 275 Rep Power: 14 Hi! I never tried this stuff, but I read somewhat about it earlier... are you sure about those boundary conditions? If I understood correctly, your cost function should come into the BC's for the adjoint eqs (if the cost function is described as a integral function over the domain). Check 'eq' 44-48 in C. Othmer, Int. J. Numer. Meth. Fluids 2008; 58:861–877 Regard, K

 February 17, 2011, 08:59 #3 Senior Member   David Boger Join Date: Mar 2009 Location: Penn State Applied Research Laboratory Posts: 146 Rep Power: 10 Jens, Did the equations converge? __________________ David A. Boger

 February 17, 2011, 09:34 #4 New Member   Join Date: Jul 2009 Posts: 10 Rep Power: 10 Hi, Thanks for the replies. @Kalle I see your point and you are right, the BC's are one problem to solve and the equations are very sensitive to the BC's but the problem is ... that leads me to @boger No, that is the "main" problem/issue. The normal velocity converge but "adjoint U" dont converge. The problem is, if i print the divergence of adjoint velocity the values are very hight (16.xx or 0.1) but the priority/task of the pressure correction is the divergence of adjoint U is equal to zero. Well, I think the first problem to solve is that the pressure correction solve -> div(adjoint U) = 0. Isn't it? The question is, is there a term missing or something else? Regards, Jens

 March 10, 2011, 02:47 #5 Senior Member   Fumiya Nozaki Join Date: Jun 2010 Location: Yokohama, Japan Posts: 217 Blog Entries: 1 Rep Power: 11 Hi Jens, Is your pressure equation right? I think the right hand side of this equation is the divergence of the adjoint velocity field. Regards, Fumiya

 March 10, 2011, 08:14 #6 Senior Member   David Boger Join Date: Mar 2009 Location: Penn State Applied Research Laboratory Posts: 146 Rep Power: 10 Good point, Fumiya - you're correct! __________________ David A. Boger

 March 10, 2011, 08:49 #7 New Member   Join Date: Jul 2009 Posts: 10 Rep Power: 10 Thanks for your help and hints. I got also a few hints by C. Othmer and the problem was the pressure equation. Last edited by Jens; March 14, 2011 at 12:39.

 March 10, 2011, 22:49 #8 Senior Member   Fumiya Nozaki Join Date: Jun 2010 Location: Yokohama, Japan Posts: 217 Blog Entries: 1 Rep Power: 11 In my calculations, the continuity error of the adjoint velocity field does not drop compared to that of the primal velocity field. 1) Though there may be problems in my code, do the adjoint equations have this tendency? 2) Are the adjoint equations sensitive to the boundary conditions? Do they converge with the same boundary conditions as the primal ones? I would be grateful if you could share findings from your computations with the original solver from Dr. Othmer. Regards, Fumiya

March 11, 2011, 04:36
#9
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Join Date: Jul 2009
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Quote:
 Originally Posted by fumiya 1) Though there may be problems in my code, do the adjoint equations have this tendency? 2) Are the adjoint equations sensitive to the boundary conditions? Do they converge with the same boundary conditions as the primal ones?
The second problem was the boundary conditions ("kalle" his hint was right). You need special boundary conditions derived from the adjoint equations and the cost function on the boundary.

Regards,
Jens

March 12, 2011, 06:55
#10
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BastiL
Join Date: Mar 2009
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Quote:
 Originally Posted by Jens You need special boundary conditions derived from the adjoint equations and the cost function on the boundary
Jens,

thanks for the findings. How do these BCs look like?
Would you mind posting your final case and solver? Thanks.

Regards Bastian.

March 13, 2011, 11:39
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Quote:
 Originally Posted by bastil Jens, thanks for the findings. How do these BCs look like? Would you mind posting your final case and solver? Thanks. Regards Bastian.
Unfortunately, I cant.

Regards,
Jens

Last edited by Jens; March 14, 2011 at 12:40.

 March 14, 2011, 22:45 #12 Senior Member   Fumiya Nozaki Join Date: Jun 2010 Location: Yokohama, Japan Posts: 217 Blog Entries: 1 Rep Power: 11 I would be grateful if you could post contour plots of the adjoint pressure and velocity fields for a simple duct when the cost function is dissipated power and flow is laminar. I would like to use these data for comparison with my results. I will prepare a case if it could save your work. Regards, Fumiya Last edited by fumiya; March 16, 2011 at 02:12.

March 16, 2011, 02:52
#13
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Fumiya Nozaki
Join Date: Jun 2010
Location: Yokohama, Japan
Posts: 217
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Rep Power: 11
I calculated surface sensitivities according to Dr. Othmer's article
when the cost function is dissipated power. In this calculation,
outlet boundary conditions are not properly imposed. I have to
implement new boundary conditions to obtain more precise results.

Regards,
Fumiya
Attached Images
 surface_sensitivity.jpg (18.5 KB, 123 views)

Last edited by fumiya; March 18, 2011 at 04:11.

 June 12, 2011, 21:09 #15 Senior Member   Fumiya Nozaki Join Date: Jun 2010 Location: Yokohama, Japan Posts: 217 Blog Entries: 1 Rep Power: 11 I have run several cases and found it difficult to obtain a converged solution. I think it is related to the adjoint transpose convection term. What should I do to improve convergence of the adjoint equations? Best regards, fumiya

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