The adjoint mehod for automotive optimisation using a sphericity based morpher

A robust workflow for shape optimisation of internal and external flows with application to automotive design is demonstrated in this paper. A gradient based approach is presented, in which the surface sensitivity with respect to the flow variables is computed with the continuous adjoint method. For aerodynamic shape optimisation cases, mesh displacement algorithms are indispensable in order to avoid re-meshing the updated geometry in each optimisation step. Keeping the same mesh topology at every optimisation cycle secures gradient consistency and the possibility to use the previous solution as initial conditions in order to converge the CFD equations faster. Simple mesh displacement algorithms, such as the spring analogy, run into problems under complex surface deformations. Thus a mesh optimisation approach can be proved to be more robust as it copes better with complex elements optimising also the base mesh. In this paper the mesh displacement algorithm is based on sphericity, which quantifies the mesh quality. Solving an extra optimisation problem for the maximisation of the sphericity value, results in the new internal mesh nodes positions. The methodology is heuristic in nature in that it does not consider known numerical quality metrics explicitly. It has shown however to be exceptionally robust and effective allowing the maintenance of high cell quality even during extreme deformation events. The suggested method is applied to automotive test cases of internal and external aerodynamics. In such cases, the use of a robust morpher which preserves geometry features and delays mesh quality deterioration is found to be crucial.