Partitioned Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

We consider the fluid-structure interaction problem arising in haemodynamic applications. The finite elasticity equations for the vessel are written in Lagrangian form, while the Navier-Stokes equations for the blood in Arbitrary Lagrangian Eulerian form. The resulting three fields problem (fluid/ structure/ fluid domain) is formalized via the introduction of three Lagrange multipliers and consistently discretized by p-th order backward differentiation formulae (BDFp). We focus on partitioned algorithms for its numerical solution, which consist in the successive solution of the three subproblems. We review several strategies that all rely on the exchange of Robin interface conditions and review their performances reported recently in the literature. We also analyze the stability of explicit partitioned procedures and convergence of iterative implicit partitioned procedures on a simple linear FSI problem for a general BDFp temporal discretizations.