A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows.

*(English)*Zbl 1152.76025Summary: Topology optimization of fluid dynamic systems is a comparatively young optimal design technique. Its central ingredient is the computation of topological sensitivity maps. Whereas, for finite element solvers, implementations of such sensitivity maps have been accomplished in the past, this study focuses on providing this functionality within a professional finite volume computational fluid dynamics solver. On the basis of a continuous adjoint formulation, we derive the adjoint equations and boundary conditions for typical cost functions of ducted flows and present first results for two- and three-dimensional geometries. Emphasis is placed on the versatility of our approach with respect to changes in the objective function. We further demonstrate that surface sensitivity maps can also be computed with the implemented functionality, and establish their connection with topological sensitivities.

##### MSC:

76D55 | Flow control and optimization for incompressible viscous fluids |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76M12 | Finite volume methods applied to problems in fluid mechanics |

##### Software:

OpenFOAM
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\textit{C. Othmer}, Int. J. Numer. Methods Fluids 58, No. 8, 861--877 (2008; Zbl 1152.76025)

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