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The objective of this study is to highlight the effect of porosity variationin a topology optimization process in the field of fluid dynamics. Usually apenalization term added to momentum equation provides to get materialdistribution. Every time material is added inside the computational domain,there is creation of new fluid-solid interfaces and apparition of gradient ofporosity. However, at present, porosity variation is not taken account intopology optimization and the penalization term used to locate the solid isanalogous to a Darcy term used for flows in porous media. With that in mind, inthis paper, we first develop an original one-domain macroscopic model for themodelling of flow through spatially varying porous media that goes beyond thescope of Darcy regime. Next, we numerically solve a topology optimizationproblem and compare the results obtained with the standard model that does notinclude effect of porosity variation with those obtained with our model. Amongour results, we show for instance that the designs obtained are different butpercentages of reduction of objective functional remain quite close (below 4\%of difference). In addition, we illustrate effects of porosity and particlediameter values on final optimized designs.

Modelling of flow through spatially varying porous media with application to topology optimization