Multigrid Methods applied to Fluid-Structure Interaction.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2012)
Dissertation Stephen Sachs -
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|Item Type:||Ph.D. Thesis|
|Title:||Multigrid Methods applied to Fluid-Structure Interaction|
In the last decades numerical simulation of physical processes has become a standard tool in the development process in engineering. In various branches of the transportation industry, such as aeronautics or turbo machinery, as well as the industry of wind energy plants the simulation of fluid flow or structure deformation requires a dynamic response of the surrounding domain, in order to predict a correct behaviour. This demand is satisfied by the field of Fluid- Structure Interaction (FSI) simulations. One of the main challenges in the field of FSI arises from the vast amount of computing power necessary for a cou- pled simulation. Mainly two approaches are used to realize these simulations. One the one hand the monolithic approach which virtually extends the fluid and structure domains to the entire FSI domain and discretizes the problem into one system of equations. On the other hand the implicit partitioned approach, which couples the two domains by boundary conditions at an interface and solves the different problems with individual solvers. In this work the multigrid coupling (MG CPL) approach is introduced, which inherits the flexibility of the implicit partitioned approach while enhancing towards the monolithic approach by using the coupling iterations as smoother for a geometric multigrid method. A MG CPL approach is implemented into the existing FSI framework at the Fachge- biet Numerische Berechnungsverfahren im Maschinenbau. The correctness and the run time of this implementation is validated by various computations. The superiority of the MG CPL in comparison to the implicit partitioned approach is shown on several discretizations and time step sizes. The linear performance of the multigrid solver for the FSI problem, as well as the stabilizing effect of closer coupling can be shown. Furthermore the extrapolation of forces in an unsteady FSI simulation is in- troduced. In contrast to common methods it extrapolates the forces acting on the structure domain and not the displacements acting on the fluid domain. Hence, in an implicit partitioned approach only half a FSI iteration is extrap- olated and the other half is computed, resulting in more physically reasonable starting point for the computations in the current time step. The superiority of the force extrapolation compared to the displacement extrapolation is shown on different discretizations with different time step sizes and with different orders of extrapolation.
|Place of Publication:||Darmstadt|
|Classification DDC:||600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften|
|Divisions:||16 Fachbereich Maschinenbau > Fachgebiet für Numerische Berechnungsverfahren im Maschinenbau (FNB)
04 Department of Mathematics
|Date Deposited:||27 Mar 2012 10:44|
|Last Modified:||16 Sep 2015 10:05|
|Referees:||Schäfer, Prof. Dr. Michael and Ulbrich, Prof. Dr. Stefan|
|Refereed:||8 February 2012|