Diploma and Master Theses (authored and supervised):
"Moderne Numerische Methoden für Fluid-Struktur Interaktion";
Supervisor: J. Schöberl, A. Jüngel;
Institut für Analysis und Scientific Computing,
final examination: 2017-10-18.
This thesis deals with the coupling of fluid dynamics with elastic solid structure, namely the Navier-Stokes equations and the nonlinear elastic wave equation, which is due to the different types of these PDEs a challenging problem.
Two different discretizations for the Navier-Stokes equations are discussed: the popular Taylor-Hood elements and the H(div)-conforming Hybrid Discontinuous Galerkin method, which ensures exact divergence-freeness.
For the elastic wave equation a standard Newmark method is used and a new H(curl)- conforming method is introduced. Therefore, an additional variable is needed: the time derivative of the momentum, which is in the dual space of H(curl).
The Arbitrary Lagrangian Eulerian description is well understood for H1-conforming methods, where the mesh velocity appears in the Navier-Stokes equations. For H(div)- conforming schemes, however, the ALE method is more involved and an additional term appears, which plays a crucial role.
The methods are implemented in NGS-Py, which is based on the finite element library Netgen/NGSolve and tested with proper examples.
Finite Elements / Fluid Sturcture Interaction
Created from the Publication Database of the Vienna University of Technology.