A Continuous Adjoint Cut-Cell Formulation for Topology Optimization of Fluid Systems with One or Two Fluids and Conjugate Heat Transfer

This paper is in the field of adjoint–based Topology Optimization (TopO) for flow systems with one or two fluids and Conjugate Heat Transfer (CHT). It proposes a cut–cell method (cutCellTopO) and compares it with the widely used density–based TopO (denTopO). In cutCellTopO, topological changes are still controlled by an artificial impermeability field \(\alpha \) (design variables) indicating the presense of fluid or solid material, based on which the Fluid Solid Interface (FSI) is computed and cut–cells are generated. The proposed method imposes accurate boundary conditions along the FSI, thus eliminating spurious flow leakage into the solidified areas. Derivatives of objective functions and constraints w.r.t. the FSI nodal positions are computed based on the continuous adjoint method. These are, then, transformed into Sensitivity Derivatives (SDs) w.r.t.  \(\alpha \) via the differentiation of the cut–cell creation process. For both methods, consistent discretization schemes for the continuous adjoint PDEs are derived and implemented. These are based on the “Think Discrete – Do Continuous” (TDDC) adjoint method; the latter computes SDs of the same accuracy as discrete adjoint, while retaining the advantages of continuous adjoint.