Fluid-structure interaction with an application to a body immersed and anchored in a fluid flow

Abstract

In this paper, an implicit coupling algorithm for fluid-structure interaction problems with under-time steps for the solid is presented. Its implementation on two configurations is achieved by using the CASTEM finite-elements code. First, the free oscillations of a cylinder in an annular fluid domain where its movement is determined by the coupled fluid-solid action is considered in the case of viscous fluid. It should be noted that the implicit coupling algorithm gives the best prediction of the structure oscillations. The under-time steps for the solid are introduced in order to obtain better results. Then, an application whose final objective is to model a floating barrage is studied. The main goal of this application is to predict the displacements of a ring completely immersed and anchored by a cable to the lower boundary of the fluid domain. The finite-element discretization of the Navier-Stokes equations in the ALE formulation is used Keywords: fluid-structure interaction, arbitrary Lagrangian-Eulerian method (ALE), moving boundaries 1. Introduction. The applications where fluid-structure interaction phenomena occur are numerous: aerodynamics [9], hydrodynamics, biomechanics [17, 10], nuclear safety, environmental protection [2], etc. Many examples can be cited: flow around an antipollution floating barrage, flow around a boat, blood flow in the arteries, flow around an airfoil, wind influence on the apron of a bridge (as occurred in the rupture of the Tacoma bridge in 1940). There are many and various industrial and environmental applications where this phenomenon occurs. This justifies the important number of works on this class of problems during last years. This growth also comes from the development of the means of calculation which allowed the implementation of algorithms in fluid-structure interaction [8].The application of these methods for modeling the antipollution floating barrage makes possible a better prediction of its behavior in real situation. The study of this typical problem of fluid-structure interaction, which imposes many difficulties, consists to treat the problem by taking into account the contribution of all parameters of the system. Thus, it will be necessary to model the structure, the flow, the fluid-structure interaction, the anchorage (cable), the free surface.The general context of this study is to develop a numerical tool by using the CASTEM finite-element code, through which such a problem can be apprehended in its global nature. In the paper, only a preliminary result is presented. The use of CASTEM to develop a numerical tool for study of the fluid-structure interaction problems is very interesting. Indeed, CASTEM has a proper language (GIBIANE) which makes it possible to establish the link between the fluid code and the structure code in the same environment. Thus, it is not necessary to develop a particular interface between two distinct codes as it is usually done.The proposed fluid-structure coupling algorithm is an alternative of the implicit scheme suggested in [1]....