Numerical simulation and analysis of multiscale interface coupling between a poroelastic medium and a lumped hydraulic circuit: comparison between functional iteration and operator splitting methods

We consider a multiscale problem modeling the flow of a fluid through a deformable porous medium, described by a system of partial differential equations (PDEs), connected with a lumped hydraulic circuit, described by a system of ordinary differential equations (ODEs). This PDE/ODE coupled problem includes interface conditions enforcing the continuity of mass and the balance of stresses across models at different scales. In the present article, we address questions related to the solution methods of the PDE/ODE coupled problem via staggered algorithms, focusing on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the interface conditions. We provide sufficient conditions for the convergence of functional iterations and prove that the energy-based operator splitting method is unconditionally stable with respect to the size of the time discretization step.