Level-set based Topology optimization using the Continuous Adjoint Method

In this paper, the development and application of the continuous adjoint of the incompressible Navier-Stokes coupled with the level-set method applied to topology optimization, is presented. The main focus of the paper is the representation and the evolution of the
surface (interface between solid and fluid) via the level-set method. In this approach, the design variables are the signed distances between the cell centers and the interface. In the first step, the surface sensitivity derivatives are extended towards the normal direction of the interface, by solving the velocity extension equation. In the second step, the interface is evolved by solving
a transport equation. After the evolution, the level-set field is no longer a signed distance field and as a result, has to be reinitialised as part of the final step. The main advantage of the level-set method is the computation of the curvature through the design variables. In this approach, curvature limitation is used as an objective function and can be minimized or maximized, which makes the final geometries smoother and more manufacturable. The presented method is applied in several industrial cases to show its efficacy.