koelke07-COLLOQUE

This contribution discusses a weighted residual based approach for the numerical analysis of fluid flow around flexible thin-walled structures. The presented method enables the investigation of flow-induced vibrations of strongly coupled systems involving large structural motion and deformation of multiple flow-immersed solid objects. The fluid is modeled in terms of the incompressible Navier-Stokes equations. The current configuration of the thin structure of linear elastic material with nonlinear kinematics is mapped to the flow domain 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 fluid weak form is performed on a space-time finite element discretization. The strong coupling of the multi-field problem is ensured by distributed Lagrange multipliers. Finally, the proposed formulation and discretization technique leads to a monolithic algebraic system.

Embedding a thin-walled structure into the flow field results in non-smooth fields of the physical state variables of the fluid. The characteristics of the non-smooth solution depend mainly on geometrical properties and the modeling of coupling conditions between fluid and structure. Within this work weak and strong discontinuities in the pressure and velocity solution to the flow are under consideration. Based on the concept of the partition of unity and the extended finite element method (XFEM), the space-time approximations of the fluid pressure and velocity are properly enriched to capture resulting weakly and strongly discontinuous solutions. This leads to the introduced enriched space-time (EST) method for applications in fluid-structure interaction. Numerical examples of fluid-structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems. Several test cases demonstrate the application of the proposed technique flow-induced vibrations and the inflation of thin-walled structures where traditional mesh moving strategies often fail.