We briefly describe a setting of a non-linear fluid-structure interaction problem and its solution in the finite element software package deal.II. The fluid equations are transformed via the ALE map (Arbitrary Lagrangian Eulerian framework) to a reference configuration. The mapping is constructed using the biharmonic operator. The coupled problem is defined in a monolithic framework and serves for unsteady (or quasi-stationary) configurations. Different types of time stepping schemes are implemented. The non-linear system is solved by a Newton method. Here, the Jacobian matrix is build up by exact computation of the directional derivatives. The implementation serves for the computation of the fluid-structure benchmark configurations proposed by J. Hron and S. Turek.
|Faculties / Institutes:||The Faculty of Mathematics and Computer Science > Department of Applied Mathematics|
|Controlled Keywords:||Fluid-Struktur-Wechselwirkung, Finite-Elemente-Methode, Implementierung|
|Uncontrolled Keywords:||Monolithic Framework , Arbitrary Lagrangian EulerianFluid-Structure Interaction , Finite Element Method , Monolithic Framework , Arbitrary Lagrangian Eulerian , Implementation|