A monolithic fluid–structure interaction approach for multiscale flows with deformable porous media

A novel monolithic interphase coupling approach for multiscale fluid–solid interactions is proposed. This approach utilizes one-field equations for both fluid flow and solid dynamics, with the interphase coupling accurately depicted through the inclusion of an analytical penalization term that accounts for the existence of the other phase. A factor is included to account for the impact of heterogeneity of unresolved structures. After describing how to set this heterogeneity factor, the method is comprehensively validated by predicting the settling process of various types of porous structures and, in a final step, flow-induced solid deformation in realistic porous media. The approach proves to be accurate for resolving the interactions between fluids and complex porous structures across distinct scales. Moreover, it shows advantages over the traditional Darcy–Brinkmann–Stokes approach in resolving local heterogeneity-related characteristics, such as preferential flows and variations in solid motion. Overall, this method shows great potential for resolving complex multiscale flows coupled to solid mechanics in realistic engineering applications.