The Vertex Morphing method for node-based shape optimization

The Vertex Morphing method, a consistent surface control approach for shape optimization is presented. This method introduces a control field and a map that relates it to the geometry field. The optimization problem is solved in the control space and the map is defined such that both surface smoothness and mesh regularity criteria are satisfied simultaneously and synchronously in the geometry field. The control field is discretized with the same discretization as the one of the geometry, which leads to the richest design space possible for optimization of a discrete geometry. The capabilities of the Vertex Morphing method are evaluated within an adjoint based CFD shape optimization workflow. Several engineering cases mainly from automotive industry are tested. The method has shown significant success in performance, efficiency and robustness even for problems with extreme geometrical complexities and millions of design parameters for applications in structural as well as fluid mechanics and their combination.