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Absence of a term in adjointShapeOptimizationFoam outlet boundary conditions

Hi Foamers,

I have a question about boundary conditions of adjointShapeOptimizationFoam. In particular, following Othmer's procedure in A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows, boundary conditions for the Outlet are:

$q = \textbf{u} \cdot \textbf{v} + u_n v_n + \nu (\textbf{n} \cdot \nabla) u_n + \frac{\partial J_{\Gamma}}{v_n}$

$0 = v_n \textbf{u}_t + \nu (\textbf{n} \cdot \nabla) \textbf{u}_t + \frac{\partial J_{\Gamma}}{\textbf{v}_t}$

but I can't find $\nu (\textbf{n} \cdot \nabla) \textbf{u}_t$ and $\nu (\textbf{n} \cdot \nabla) u_n$ in adjointOutletPressureFvPatchScalarField.C and adjointOutletVelocityFvPatchScalarField.C.

Are they neglected because they are irrelevant or is simply the normal gradient of adjoint velocity forced to be null?

Best regards,
Roberto

Hi Roberto!
I have exactly the same doubt, since in the code:

Code:

operator==((phiap/patch().magSf() - 1.0)*phip/patch().magSf() + (Up & Uap));

and

Code:

vectorField::operator=(phiap*patch().Sf()/sqr(patch().magSf()) + UtHat);

there isn't any "normal gradient" term.

Let's hope for some help :)

Domenico

Hi,

You can find how to implement these terms in the following document:

Description of adjointShapeOptimizationFoam and how to implement new objective functions
http://www.tfd.chalmers.se/~hani/kur...ortAdjoint.pdf

Best regards,
Fumiya