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 November 1, 2011, 00:26 #2 Super Moderator   Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 342 Blog Entries: 6 Rep Power: 17 If on some part of boundary, u is fixed by the boundary condition, then du=0 on that part. If u is not specified on some part S of boundary, and you have a term like int(S)(X du) then set X=0 on S. The idea is simply to get rid of all the variations in the primal quantities.

 November 1, 2011, 01:50 #3 Senior Member     Fumiya Nozaki Join Date: Jun 2010 Location: Yokohama, Japan Posts: 266 Blog Entries: 1 Rep Power: 17 Thanks for reply. I understand your comment. It says in this article that "δu=0 on S(solid boundaries to be optimized) and on the outflow (Γout)". I think that δu=0 is valid on S because of the dirichlet (no-slip) boundary condition but I can't understand why δu=0 on the outlet boundary. I think dirichlet conditions are not imposed on the velocity at the outlet when solving the flow. Q) Is δu=0 valid on the outlet boundary? I have another question. Q) Could someone understand the meaning of the following statement? "δu is the test function associated to the adjoint velocity, then it is zero wherever ψu(adjoint velocity) is prescribed"

 November 1, 2011, 02:33 #4 Super Moderator   Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 342 Blog Entries: 6 Rep Power: 17 Can you indicate page/paragraph in that paper about which you have the question ?

 November 1, 2011, 03:04 #5 Senior Member     Fumiya Nozaki Join Date: Jun 2010 Location: Yokohama, Japan Posts: 266 Blog Entries: 1 Rep Power: 17 Please look at the paragraph under the equation (19) on page three. In this paragraph the adjoint boundary conditions are discussed.

 November 1, 2011, 03:41 #6 Super Moderator   Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 342 Blog Entries: 6 Rep Power: 17 On outflow boundary, u must come from the solution, it is not prescribed. Hence we dont know du. So to get rid of du on outflow boundary, set Psi_u=0. Thats how I look at it.

 November 1, 2011, 11:09 #7 Senior Member     Fumiya Nozaki Join Date: Jun 2010 Location: Yokohama, Japan Posts: 266 Blog Entries: 1 Rep Power: 17 Could someone tell me why the following statement is valid? "δu is the test function associated to the adjoint velocity, then it is zero wherever ψu(adjoint velocity) is prescribed"