# Simcenter STAR-CCM+ How to compute the average of the Surface Sensitivity in ad Adjoint Simulation

2022-07-04T14:51:57.000-0400
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## Summary

The aim of this article is to show a procedure to compute an averaged field starting from an asymmetric distribution of the quantity of interest. The procedure can be applied to compute the average value of the surface sensitivity field to make the Adjoint solution suitable for an industrial case.

## Details

Let's imagine we are running an external aero case on a full car and we are using the Adjoint solution to morph the rear spoiler, to improve its efficiency.
Due to the turbulent structures, the flow field might not be perfectly symmetric with respect to the longitudinal plane. As a consequence of this the sensitivity, the field computed on the component might be asymmetric.
The displacement field used for the Morph Surface Mesh operation is a function of the sensitivity field and will then lead to an asymmetric shape of the rear spoiler, preventing these results to be used for an industrial case.

In this article a very simple test case will show how to compute an average field starting from an asymmetric distribution of a generic quantity. The same procedure can be then applied to compute the mean Sensitivity field of an Adjoint simulation.

Let's consider the asymmetric field function

-D = abs(\$\${Position})+(\$\${Position}<0)*0.2*\$\${Position}  Using a Data Mappers with the following settings:  Simcenter STAR-CCM+ will be able to create a new field function (mappedD) as mirror of the original one (_D): At this point the average of mappedD and _D can be computed via the definition of the following field function:

_avgD = (\${_D}+\${Mapped_D})/2 _D and _avgD field functions can be converted into vectors via the definition of the following functions:

_D_vector = \${_D}*\$\${Normal}

_avgD_vector = \${_avgD}*\$\${Normal}

Now these functions can be used to define the Morph Surface Displacements.

Images below show the differences between the displacements applied. 