*(English)*Zbl 1195.74212

Summary: The paper introduces a weighted residual-based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures. The presented method enables one to treat strongly coupled systems involving large structural motion and deformation of multiple-flow-immersed solid objects.

The fluid flow is described by the incompressible Navier-Stokes equations. The current configuration of the thin structure of linear elastic material with nonlinear kinematics is mapped to the flow using the zero iso-contour of an updated level set function. The formulation of fluid, structure and coupling conditions uniformly uses velocities as unknowns. The integration of the weak form is performed on a space – time finite element discretization of the domain. Interfacial constraints of the multi-field problem are ensured by distributed Lagrange multipliers. The proposed formulation and discretization techniques lead to a monolithic algebraic system, well suited for strongly coupled fluid – structure systems. Embedding a thin structure into a flow results in non-smooth fields for the fluid. Based on the concept of the extended finite element method, the space – time approximations of fluid pressure and velocity are properly enriched to capture weakly and strongly discontinuous solutions. This leads to the present enriched space – time (EST) method. Numerical examples of fluid – structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems. The test cases demonstrate the application of the proposed technique to problems where mesh moving strategies often fail.