Reducing parameter tuning in topology optimization of flow problems using a Darcy and Forchheimer penalization

In density-based topology optimization of flow problems, flow in the solid domain is generally inhibited using a penalization approach. Setting an appropriate maximum magnitude for the penalization traditionally requires manual tuning to find an acceptable compromise between flow solution accuracy and design convergence. In this work, three penalization approaches are examined, the Darcy (D), the Darcy with Forchheimer (DF), and the newly proposed Darcy with filtered Forchheimer (DFF) approach. Parameter tuning is reduced by analytically deriving an appropriate penalization magnitude for accuracy of the flow solution. The Forchheimer penalization is found to be required to reliably predict the accuracy of the flow solution. The state-of-the-art D and DF approaches are improved by developing the novel DFF approach, based on a spatial average of the velocity magnitude. In comparison, the parameter selection in the DFF approach is more reliable, as convergence of the flow solution and objective convexity are more predictable. Moreover, a continuation approach on the maximum penalization magnitude is derived by numerical inspection of the convexity of the pressure drop response. Using two-dimensional optimization benchmarks, the DFF approach reliably finds accurate flow solutions and is less prone to converge to inferior local optima.