Coupling Different Discretizations for Fluid Structure Interaction in a Monolithic Approach

You are cordially invited to attend the PhD Dissertation Defense of Johannes Steiner on Tuesday, November 25th 2014 at 17h00 in room 250 (USI main building)

Abstract:
In this thesis we present a monolithic coupling approach for the simulation of phenomena involving interacting fluid and structure using different discretizations for the sub-problem.
For many applications in fluid dynamics, the Finite Volume method is the first choice in simulation science. Likewise, for the simulation of structural mechanics the Finite Element method is one of the most, if not the most, popular discretization method.
However, despite the advantages of these discretizations in their respective application domains, monolithic coupling schemes have so far been restricted to a single discretization for both sub-problems.
We present a fluid structure coupling schema based on a mixed Finite Volume/Finite Element method that combines the benefits of these discretizations.
An important challenge in coupling fluid and structure is the transfer of forces and velocities at the fluid structure interface in a stable and efficient way. In our approach this is achieved by means of a fully implicit formulation, i.e., the transfer of forces and displacements is carried out in a common set of equations for fluid and structure.
We assemble the two different discretizations for the fluid and structure sub-problems as well as the coupling conditions for forces and displacements into a single large algebraic system.
Since we simulate real world problems, as a consequence of the complexity of the considered geometries, we end up with algebraic systems with a large number of degrees of freedom. This necessitates the use of parallel solution techniques.
Our work covers the design and implementation of the proposed heterogeneous monolithic coupling approach as well as the efficient solution of the arising large nonlinear systems on distributed memory supercomputers.
We apply Newton's method to linearize the fully implicit coupled nonlinear fluid structure interaction problem. The resulting linear system is solved with a Krylov subspace correction method. For the preconditioning of the iterative solver we propose the use of multi-level methods. Specifically, we study a multigrid as well as a two-level restricted additive Schwarz method.
We illustrate the performance of our method on benchmark examples and compare the afore mentioned different preconditioning strategies for the parallel solution of the monolithic coupled system.

Dissertation Committee:

• Prof. Rolf Krause, Università della Svizzera italiana, Switzerland (Research Advisor)
• Prof. Igor Pivkin, Università della Svizzera italiana, Switzerland (Internal Member)
• Prof. Olaf Schenk, Università della Svizzera italiana, Switzerland (Internal Member)
• Prof. Arnold Reusken, RWTH Aachen University, Germany (External Member)
• Prof. Axel Klawonn, Universität Duisburg/Essen, Germany (External Member)