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We develop a computational model to study the interaction of a fluid with aporoelastic material. The coupling of Stokes and Biot equations represents aprototype problem for these phenomena, which feature multiple facets. On onehand it shares common traits with fluid-structure interaction. On the otherhand it resembles the Stokes-Darcy coupling. For these reasons, the numericalsimulation of the Stokes-Biot coupled system is a challenging task. The need oflarge memory storage and the difficulty to characterize appropriate solvers andrelated preconditioners are typical shortcomings of classical discretizationmethods applied to this problem. The application of loosely coupled timeadvancing schemes mitigates these issues because it allows to solve eachequation of the system independently with respect to the others. In this workwe develop and thoroughly analyze a loosely coupled scheme for Stokes-Biotequations. The scheme is based on Nitsche's method for enforcing interfaceconditions. Once the interface operators corresponding to the interfaceconditions have been defined, time lagging allows us to build up a looselycoupled scheme with good stability properties. The stability of the scheme isguaranteed provided that appropriate stabilization operators are introducedinto the variational formulation of each subproblem. The error of the resultingmethod is also analyzed, showing that splitting the equations pollutes theoptimal approximation properties of the underlying discretization schemes. Inorder to restore good approximation properties, while maintaining thecomputational efficiency of the loosely coupled approach, we consider theapplication of the loosely coupled scheme as a preconditioner for themonolithic approach. Both theoretical insight and numerical results confirmthat this is a promising way to develop efficient solvers for the problem athand.

Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach