Asymptotically Proved Numerical Coupling of a 2D Flexural Porous Plate with the 3D Stokes Fluid

A numerical workflow for a linear multiscale fluid-structure interaction (FSI) problembetween 3D Stokes flow and an effective porous, homogenized 2D plate is presented. The underlyingeffective FSI model is obtained from the method of two-scale convergence for thin perforated andperiodic filter structures, performed in earlier works. On the micro scale, the numerical workflowcomprises the computation of the filter structure's effective homogenized stiffness tensors utilizinga beam finite element formulation, as well as the computation of the permeability tensor. On themacro scale, a monolithic finite element formulation for the FSI problem with conforming elementsis derived. Numerical results and sensitivity studies demonstrating the influence of design variationson the micro scale on the FSI solution are presented for woven filter structures.