Keywords: multiscale modelling, porous media, advection-diffusion, asymptotic homogenization, semipermeable interface, fluid-structure interaction, dynamic permeability.

The paper is aimed to explore influence of the fluid-structure interaction (FSI) in soft porous structure on the flow and transport of a species agent to the solid while taking into account the interface permeability depending on the wall shear stress due to the flow. The modelling is based on the two-scale homogenization of the coupled FSI and the advection-diffusion problems. The solid skeleton is composed of rigid frame supporting a very compliant elastic, or poroelastic structure. The solid elasticity progressively less stiff with decreasing microstructure scale. This leads to the FSI tight coupling at the micro-scale, in contrast with the ``standard''case of a given fixed elasticity. For the scale decoupling of the limit advection term in the two-scale trasport equation, the spectral based decomposition is proposed to avoid the use of the Laplace transformation of the product of two time functions. Finite element method is applied to solve both the micro- and macrosscopic problems of the flow and transport. Convolution kernels approximations are based on the Prony series to provide efficient integration schemes. Numerical illustrations are reported.

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