Robust Quasi-Newton Methods for Partitioned Fluid-Structure Simulations

In recent years, quasi-Newton schemes have proven to be a robust and efficient way for the coupling of partitioned multi-physics simulations in particular for fluid-structure interaction. The focus of this work is put on the coupling of partitioned fluid-structure interaction, where minimal interface requirements are assumed for the respective field solvers, thus treated as black box solvers. The coupling is done through communication of boundary values between the solvers. In this thesis a new quasi-Newton variant (IQN-IMVJ) based on a multi-vector update is investigated in combination with serial and parallel coupling systems. Due to implicit incorporation of passed information within the Jacobian update it renders the problem dependent parameter of retained previous time steps unnecessary. Besides, a whole range of coupling schemes are categorized and compared comprehensively with respect to robustness, convergence behaviour and complexity. Those coupling algorithms differ in the structure of the coupling, i. e., serial or parallel execution of the field solvers and the used quasi-Newton methods. A more in-depth analysis for a choice of coupling schemes is conducted for a set of strongly coupled FSI benchmark problems, using the in-house coupling library preCICE. The superior convergence behaviour and robust nature of the IQN-IMVJ method compared to well known state of the art methods such as the IQN-ILS method, is demonstrated here. It is confirmed that the multi-vector method works optimal without the need of tuning problem dependent parameters in advance. Furthermore, it appears to be especially suitable in conjunction with the parallel coupling system, in that it yields fairly similar results for parallel and serial coupling. Although we focus on FSI simulation, the considered coupling schemes are supposed to be equally applicable to various kinds of different volumeor surface-coupled problems.