
Multiscale topology optimization of fluid devices by the dehomogenization method: challenges and new developments
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In the context of the tremendous progresses of additive manufacturing, there is a growing interest for optimizing multiscale systems featuring locally periodic patterns. The recent years have been marked by the arising of dehomogenization methods for the design of multiscale lattice structures, exploiting homogenization theory to avoid fine scale simulations. However, these developments have been mostly confined to the optimization of mechanical structures. This presentation we will discuss recent research and theoretical challenges about the extension of multiscale topology optimization methods for thermal and fluid systems. We will notably mention an extension of dehomogenization methods to fluid systems, recent asymptotic results for periodic fluid media, the use of machine learning for interpolating homogenized tensors, and new numerical perspectives for taking into account the influence of the inlet and outlet flow regions when optimizing the shape of periodic ducts.