Abstract
AbstractThe 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 non‐linear 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. Copyright © 2007 John Wiley & Sons, Ltd.
Highlights
The evaluation of fluid–structure interaction effects and the investigation of governing physical phenomena associated with coupled systems are always challenges in problems arising in the field of aero- and hydro-elasticity, life-sciences or bio-engineering
The present paper proposes an elegant way to treat a fluid–structure interaction problem in the case of thin immersed structures
The time axis is included in the mesh discretization for both fluid and structures leading to a space–time discretization
Summary
The evaluation of fluid–structure interaction effects and the investigation of governing physical phenomena associated with coupled systems are always challenges in problems arising in the field of aero- and hydro-elasticity, life-sciences or bio-engineering. Combined with a finite element discretization of both domains, a conservative coupling can be achieved by the compatibility of the two meshes (geometry) and approximation (physics) at the common fluid–structure interface This condition may introduce severe complications, e.g. fluid mesh distortions (see Figure 1), if mesh-moving strategies are applied. The extended finite element concept has been applied by Kolke et al in conjunction with an enriched space–time (EST) finite element discretization [18] of two-liquid flow problems including surface tension, where discontinuous pressure solutions at evolving and level set-captured interfaces are represented by an extended approximation in space–time This approach has been discussed by Chessa and Belytschko [19, 20] to arbitrary discontinuities based on space–time finite elements and was realized for spatially one-dimensional shock-dominated problems.
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