Jemcov, A., Stephens, D., and Sideroff, C., "Application of Time Symmetry Preserving Adjoint Solver in External Car Aerodynamics," SAE Technical Paper 2014-01-0412, 2014, doi:10.4271/2014-01-0412.
Adjoint equations for the incompressible turbulent Navier-Stokes equations are presented. The main characteristic of this adjoint formulation is that it is time symmetry preserving thus kinetic energy conservative. The newly formulated equations were applied to the computation of surface shape sensitivities of an Australian V8 supercar. Three cases for the shape sensitivity were considered: sensitivity of the body, mirror, and the rear wing of the vehicle. Shape derivatives indicated that regions of large curvature, sudden changes and sharp features are responsible for the majority of the surface force sensitivity. Vector plots show the direction of change in shape required to increase the surface force. In addition, examining the rear wing shape derivatives reveal a close correlation to the flow features.