An Adjoint‐Based Solver with Adaptive Mesh Refinement For Efficient Design of Coupled Thermal‐Fluid Systems

A multi-objective continuous adjoint strategy based on the superposition of boundary functions for topology optimization of problems where the heat transfer must be enhanced and the dissipated mechanical power controlled at the same time, has been here implemented in a Finite Volume (FV), incompressible, steady flow solver supporting a dynamic Adaptive Mesh Refinement (AMR) strategy. The solver models the transition from fluid to solid by a porosity field, that appears in the form of penalization in the momentum equation; the material distribution is optimized by the Method of Moving Asymptotes (MMA). AMR is based on a hierarchical non-conforming h-refinement strategy and is applied together with a flux correction to enforce conservation across topology changes. It is shown that a proper choice of the refinement criterium favors a mesh-independent solution. Finally, a Pareto front built from the components of the objective function is used to find the best combination of the weights in the optimization cycle. Numerical experiments on two- and three-dimensional test cases, including the aero-thermal optimization of a simplified layout of a cooling system, have been used to validate the implemented methodology.