A Finite Element Model for Fluid--Poroelastic Structure Interaction with Dissipative Interface

Abstract

This paper extends our prior work on interface conditions between two poroelastic domains to the case when a poroelastic domain interacts with a pure fluid. The porous medium is assumed to be deformable and modeled following mixture theory. When not in a mixture, each constituent of the porous domain is assumed to be incompressible. An arbitrary Lagrangian--Eulerian formulation is developed for both the fluid and porous domains. The fluid velocity and pressure fields are allowed to be discontinuous across the pure fluid/porous domain interface. A globally continuous displacement field is defined to represent both the deformation of the solid skeleton of the poroelastic medium and the mesh motion in the pure fluid domain. As an interface condition, the continuity of the normal component of the filtration velocity is enforced via a Lagrange multiplier. The mixture momentum jump condition is implemented so as to transfer the traction from the fluid side to the porous domain. A dissipative behavior is attributed to the interface, and the jump condition for the fluid momentum, derived from Hamilton's principle, incorporates this prescribed behavior. The model implementation is verified using the method of manufactured solutions, and a sample problem is solved to compare an inert interface with a fully dissipative one. The results show satisfactory convergence rates, while the proposed model successfully reproduces the analytical solution of a benchmark problem using conventional jump conditions. Furthermore, the findings highlight the significant influence of the selected interface model on the behavior of the system.