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An arbitrary Lagrangian Eulerian finite-element approach for fluid-structure interaction phenomena. (English) Zbl 1062.74617

Summary: The present contribution is concerned with the design of a family of consistent fluid-structure interaction algorithms based on a unique temporal and spatial discretization of the governing equations. The characterization of the moving fluid-structure interface is realized by means of the arbitrary Lagrangian Eulerian technique. The spatial discretization is performed with the finite-element method, whereby either a first-order upwind scheme or the classical second-order upwind Petrov-Galerkin technique are used to discretize the linearized fluid equations while the standard Bubnov-Galerkin method is applied to the structural equations. In order to streamline coupling, the structure is discretized in a velocity-based fashion. The temporal discretization of both the fluid and the structural equations is embedded in the generalized-\(\alpha\) framework by making use of classical Newmark approximations in time. To quantify the sources of error of the proposed algorithms, systematic studies in terms of the one-dimensional piston model problem are presented.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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