FluTO: Graded Multiscale Fluid Topology Optimization using Neural Networks

Multiscale Topology Optimization of modulated fluid microchannels based on asymptotic homogenization

“…In contrast, a rather good agreement between the full-scale and the homogenized model is reported in the alternative dehomogenization method of [53,26,68]. More accurate homogenized models should be sought to minimize physical discrepancies between the homogenized and the dehomogenized medium; for instance, a Brinkman equation featuring the inverse of the homogenized Darcy tensor as porosity coefficient is used in [53]. Future investigations could therefore seek to devise methods able to handle non-conformal mappings, and foreseeing improved homogenized descriptions of porous media.…”

“…In contrast, the variability of admissible Turing patterns seems currently rather limited to stripe or spot shapes whose geometry is controlled by the convection-reaction parameters [45]. In comparison with the alternative method of [53,54] also based on periodic homogenization, the proposed dehomogenization method is able to generate designs that are not restricted to periodic arrangements of micropillar arrays with a locally varying pattern. We note that in the latter works, the pattern can be chosen within a variety of unit cells (which theoretically could also be considered in the present framework), but these cells are projected on a (nondeformed) cartesian grid, limiting the range and the complexity of achievable designs.…”

“…Furthermore, the proposed approach based on the Darcy system (4.3) fails to capture the velocity and pressure field accurately. In contrast, a rather good agreement between the full-scale and the homogenized model is reported in the alternative dehomogenization method of [53,26,68]. More accurate homogenized models should be sought to minimize physical discrepancies between the homogenized and the dehomogenized medium; for instance, a Brinkman equation featuring the inverse of the homogenized Darcy tensor as porosity coefficient is used in [53].…”

“…The optimized designs include "gray regions" corresponding to porous parts of the design which were not dehomogenized. More recently, [53,54] proposed a multiscale TO method for the optimization of the orientations and sizes of micropillars that could be selected among a set of predefined shapes relying on a Stokes model penalized with the Darcy permability matrix obtained by periodic homogenization. Finally, [19] developed a multiscale Topology Optimization method relying on recent macroscale models obtained by the volume averaging technique, still observing large discrepancies with direct fluid simulations.…”