A fluid‐structure interaction approach with inherently fulfilled coupling conditions. Issue 1 (17th December 2018) - Schwarz, Alexander; Averweg, Solveigh; Nisters, Carina; Schröder, Jörg
Abstract: In the present contribution a fluid‐structure interaction (FSI) approach based on a mixed least‐squares finite element method (LSFEM) is introduced. The LSFEM is a variational approach for constructing finite element formulations, see e.g. [1] and [2]. In this work, the proposed FSI method is based on the formulation of mixed finite elements in terms of stresses and velocities for both the fluid and the solid regime. The conforming discretization of the stresses and velocities in the spaces H (div) and H 1, respectively, leads to the inherent fulfillment of the coupling conditions of a FSI method. The idea of the LSFEM based FSI scheme is the solution of the full problem consisting of both domains in one triangulation at the same time. The general idea on this was firstly annotated in [8]. A numerical example considering an incompressible, linear elastic solid at small deformations (compare to [3]) together with an incompressible laminar fluid flow demonstrates the applicability of the LSFEM‐FSI approach.