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Total force optimization or pressure force optimization?

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Old   July 3, 2013, 06:41
Default Total force optimization or pressure force optimization?
Roberto Pieri
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As written in the title, I would like to know if SU2 force optimization is based on this objective function:

J(S) = \int_S j (\mathbf{f}) \, ds = \int_S \mathbf{f} \cdot \mathbf{d} \, ds,


& \mathbf{f} = p \mathbf{n} - \underline{\underline{\bar{\sigma}}} \cdot \mathbf{n} \\
& p \mbox{ pressure} \\
& \underline{\underline{\bar{\sigma}}} \mbox{ tensor of viscous stresses} \\
& \mathbf{d} \mbox{ constant direction}

I found that only the pressure component of drag is reduced in the optimization framework, while friction component doesn't change.
Is this related to the absence of the tensor of viscous stresses in the equation of the shape sensitivity (eq. (35) of "Continuous Adjoint Approach for the Spalart-Allmaras Model in Aerodynamic Optimization"; Bueno-Orovio, Castro, Palacios, Zuazua) or to the definition of the objective function implemented in the code?
Another question: where can I found lines of the code where shape sensitivity is computed?
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Old   August 19, 2013, 15:54
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Thomas D. Economon
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Hi Roberto,

Indeed, the force-based optimization in SU2 is based on the form of the objective function in your post. It turns out that, if you perform some manipulations/simplifications during the adjoint derivation including substitution of the N-S equations written on the surface, you arrive at an expression for the sensitivity that does not explicitly involve the pressure or stress tensor on the surface (please see Appendix E of "Continuous Adjoint Approach for the Spalart-Allmaras Model in Aerodynamic Optimization").

The surface sensitivity is computed for inviscid flows in CAdjEulerSolver::Inviscid_Sensitivity(CGeometry *geometry, CSolver **solver_container, CNumerics *numerics, CConfig *config) and for viscous flows in CAdjNSSolver::Viscous_Sensitivity(CGeometry *geometry, CSolver **solver_container, CNumerics *numerics, CConfig *config), which can both be found in the file solver_adjoint_mean.cpp in the latest version of the code.

Hope this helps, and cheers,
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force optimization, shape sensitivity

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