A non-iterative, second-order in time approximation of fluid-structure interaction problem

We present a novel, partitioned method for the interaction between a viscous, incompressible fluid and a thin structure. The method is similar to the sequential Backward Euler - Forward Euler implementation of the Crank-Nicolson discretization scheme. The structure and fluid sub-problems are first solved using a Backward Euler scheme, and them solved using a Forward Euler scheme. The stability analysis based on energy estimates shows that the scheme is unconditionally stable. Error analysis of the semi-discrete problem yields second-order convergence in time. We will present numerical examples showing an excellent comparison of the proposed scheme to the monolithic scheme using the same time step for both methods.