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

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