[Evgeniy]

Dear su2 people,
i’m doing verification analysis of objective function gradient calculation (lift force minimization) for high-lift airfoil NLR7301 with CST design variables for incompressible flow (steady RANS) by using finite difference approach, continuous adjoint method in SU2.
The results of SU2 gradient calculation by using surface integral formulation are quite far from finite difference ones (value of design variables perturbations were extensively tested). In order to improve accuracy of gradient calculation i decided to try estimate gradient by using volume integral formulation with mesh deformation for every design variable. From SU2 documentation is not fully clear what is conservative_1 variable means (for incompressible adjoint formulation).
If we consider 2D incompressible adjoint Euler equation in non conservative form in D:
∂ψ2/∂x1 + ∂ψ3/∂x2 = 0;
u1 ∂ψ2/∂x1 + u2 ∂ψ2/∂x2 + ∂ψ1/∂x1 + u1 ∂ψ2/∂x1 + u2 ∂ψ3/∂x1 = 0;
u1 ∂ψ3/∂x1 + u2 ∂ψ3/∂x2 + ∂ψ1/∂x2 + u1 ∂ψ2/∂x2 + u2 ∂ψ3/∂x2 = 0,
where:
u1, u2 – components of velocity vector;
ψ2, ψ3 - components of adjoint velocity vector;
ψ1 – adjoint pressure.
Does conservative_1 variable equal to primitive variable ψ1 (in system above) or it’s combination of adjoint primitive variables?

Any reply would be appreciated!
Kind regards,
Evgeniy

[Evgeniy]

I think I found the answer on my question above in code, please correct me if i’m wrong.
From Cnumerics::GetInviscidArtCompProjJac() function (numerics_sructure.cpp) follows that SU2 solves the following incompressible adjoint equations:
∂ψ2/∂x1 + ∂ψ3/∂x2 = 0;
u1 ∂ψ2/∂x1 + u2 ∂ψ2/∂x2 + ∂ψ1/∂x1 = 0;
u1 ∂ψ3/∂x1 + u2 ∂ψ3/∂x2 + ∂ψ1/∂x2 = 0;
These equations are different from classical adjoint formulation presented in my first post. Apparently adjoint variable conservative_1 can be expressed as follows:
∂conservative_1/∂x1 = ∂ψ1/∂x1 + u1 ∂ψ2/∂x1 + u2 ∂ψ3/∂x1;
∂conservative_1/∂x2 = ∂ψ1/∂x2 + u1 ∂ψ2/∂x2 + u2 ∂ψ3/∂x2.
Here if my guess is correct i would like to ask another questions.
Why in SU2 use incomplete adjoint equations system for incompressible flow which obviously provide different adjoint solution from complete adjoint system?
I can imagine that incomplete system is more stable however it would be good to know how it affect on gradient accuracy and on class of problems which can be solved by using incomplete adjoint system?

I will be thankful to any reply!
Kind regards,
Evgeniy

[Evgeniy]

Hello all,
i’ve get some verification results for high-lift airfoil case. The results are attached and the description of the test case is follows.
Lift force minimization problem for two element high-lift airfoil NLR7301 at AoA=11 deg with CST design variables (12 variables per element (6 for top, 6 for bottom parts)).
Direct problem model is steady incompressible RANS equations, Re = 2.2e+06, M = 0.09.
Adjoint problem model is continuous steady incompressible viscous adjoint equations with frozen turbulence assumption.
Two types of adjoint equations were analyzed: complete system (see first post (viscous part is not presented)) and incomplete system (see second post)).
Objective function gradient was calculated by using finite difference approach (FD), complete adjoint system with volume integral formulation (adj_eq_vol_int_form); incomplete adjoint system with volume integral formulation (short_adj_eq_vol_int_form); incomplete adjoint system with surface integral formulation (short_adj_eq_surf_int_form).
As you can see from the results only complete adjoint system with volume integral formulation provide gradient close enough to finite difference one.
Does anybody experienced with similar results?
Thanks,
Evgeniy

[JPBLourenco]

Hi,

Does anyone know how to use CST method (class shape transformation) in SU2? In the configure file it's not clear how to do it. I try this configuration
DEFINITION_DV= (20, 1.0 |airfoil| 0, 1, 8) for shape optimization airfoil but nothing change in the airfoil.

I'm using the SU2 version5.0

Thanks

[fpalacios]

I think the correct number of the design variable is 51

Best,
Francisco

[fpalacios]

There is an interesting work on that topic AIAA 2017-4363 feel free to ask the authors. The surface formulation is beautiful, elegant and exact however not practical dealing with N-S flows and non-perfect grids (too affected by the accuracy of the surface gradients).
If you are planning to develop SU2 please check www.su2devsociety.org

Best,
Francisco

[Evgeniy]

Dear Francisco,
Thank you for your answer and valuable reference! I would be happy to contribute to SU2 as i have some solid and stable code!
Thanks,
Evgeniy

[JPBLourenco]

Originally Posted by fpalacios

There is an interesting work on that topic AIAA 2017-4363 feel free to ask the authors. The surface formulation is beautiful, elegant and exact however not practical dealing with N-S flows and non-perfect grids (too affected by the accuracy of the surface gradients).
If you are planning to develop SU2 please check www.su2devsociety.org

Best,
Francisco

Thank you for your suggestion. I will now examine the article which I find quite interesting and useful for my study. I'm working with N-S equation which can be a problem in that case. Thank you for the invitation. I will check and maybe join in a near future.

Best,
João Lourenço