Sensitivity maps are an indispensable tool for the design engineer since they can provide information on the favorable direction of surface displacement for reducing an objective function. Sensitivity maps are practically the sensitivity derivatives of the objective function with respect to the normal displacement of the boundary nodes and can be computed at the cost of a single flow and adjoint solution. 

Even though one could stop at the computation of the sensitivity map itself and update the car geometry manually, it is also possible to use sensitivity maps to perform an automated shape update. Both the computation of adjoint-based sensitivity maps and automated optimization loops utilizing them are implemented within the FOSS variant of OpenFOAM.

The shape of the red areas is updated based on the sensitivity map during an automated shape optimization loop.

After a few cycles of an automated shape optimization loop, drag is reduced by almost 3%. The method used to update the car shape maintains the feature lines of the baseline geometry, avoiding big deviations from the initial design. 

Normal displacement of the DrivAer surface after 8 optimization cycles. Blue areas have been displaced inwards while red ones have been moved outwards. 

The change effected by the shape optimization algorithm on the DrivAer geometry reduces drag by mainly increasing the pressure on the rear window of the car geometry and reducing the area exhibiting recirculation.

Pressure on the back side of the DrivAer car model for the baseline (left) and optimized (right) geometry.

Near wall velocity magnitude and surface LIC on the back side of the DrivAer car model for the baseline (left) and optimized (right) geometry.