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

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Topological derivatives applied to fluid flow channel design optimization problems (2016, background): “Thus, as a future work, it can be implemented a onestep approach where the governing equations and line search would be solved simultaneously [32, 18].”
Optimizing parameterized CAD geometries using sensitivities based on adjoint functions (2012, methodology): “The sensitivity map used for this model was computed using OpenFOAM [17] and an in-house adjoint analysis code the details of which are outside the scope of this paper [18, 19].”
Effective adjoint approaches for computational fluid dynamics (2019, background): “Furthermore, for an object-oriented, industrial-scale code such as OpenFOAM, even isolating the functions needed to create a single-cell residual computation is challenging.”
Topology Optimization of Turbulent Flows (2018, methodology): “Considering the topology optimization of turbulent flows, [14, 15] utilized a simplified sensitivity analysis through the so-called frozen turbulence assumption, i.”