A Second-Order in Time Approximation of Fluid-Structure Interaction Problem

We propose and analyze a novel, second-order in time, partitioned method for the interaction between an incompressible, viscous fluid and a thin, elastic structure. The proposed numerical method is based on the Crank–Nicolson discretization scheme, which is used to decouple the system into a fluid subproblem and a structure subproblem. The scheme is loosely coupled, and therefore at every time step, each subproblem is solved only once. Energy and error estimates for a fully discretized scheme using finite element spatial discretization are derived. We prove that the scheme is stable under a CFL condition, second-order convergent in time, and optimally convergent in space. Numerical examples support the theoretically obtained results and demonstrate the applicability of the method to realistic simulations of blood flow.