Least-Squares Methods for the Solution of Fluid-Structure Interaction Problems

Abstract

Different numerical methods have been proposed for the solution of partial differential equations (PDE). Most of them are based on a variational principle which recasts the PDE into an equivalent integral equation. One of the most common principles is the Galerkin method, which has some specific disadvantages for some types of PDE. In this work an alternative variational principle, the least squares finite element method, will be tested with respect to its application for transient fluid-structure interaction problems. The accurracy of different formulations which were proposed for the Navier-Stokes equations in literature will be tested. In a next step these formulations will be coupled with a standard Galerkin approach for the structure. After that a new formulation for the linear equations of elastodynamics is developed and analysed with respect to its stability and accuracy. With this formulation it is possible do develop a pure least squares formulation for the strongly coupled fluid-structure problem. Finally the different formulations are tested with respect to their accuracy and efficiency.