A discrete adjoint approach based on finite differences applied to topology optimization of flow problems

Abstract

Topology optimization methods have been vastly applied to fluid problems with different methods. In this work, the discrete adjoint (DA) approach is used in combination with a finite differences scheme to calculate the sensitivity of incompressible and compressible flow problems. The proposed methodology is especially useful for complex physical problems, where the derivation of the adjoint system can be a challenging task. The algorithm considers the finite volume model to solve the state equations, and uses an adaptive mesh refinement (AMR) scheme during the optimization to enhance the definition of the solid–fluid interface while trying to maintain a competitive computational cost. The implementation is done by using the OpenFOAM platform, which can be modified to address algorithm needs (DA and AMR). The results show an evaluation of the proposed methodology by considering traditional 2D cases of incompressible flow and exploring compressible flow cases with meshes using different cell types and 3D models.