A Time Domain Boundary Element Method for Fluid‐Structure Interaction Analysis on a Discontinuous Surface

Kurzfassung

In this thesis, the development of the two‐dimensional time domain solver cBEM for modeling linear hydrodynamic problems is described. The approach was based on Potential Flow Theory and applied Boundary Integral Equations with that the governing Boundary Value Problem was solved and the inter‐ actions of body and surface gravity waves were modeled. The embedding of the High‐Order Spectral procedure into the Boundary Element Method in the symmetric Galerkin formulation represents an innovative coupling method for the treatment of hydrodynamic problems.The explicit account of a surface discontinuity represented by the body in the free surface boundary domain, the strategy of incorporating the High‐Order Spectral approach in the Boundary Element Method, and the development of suited desingularization techniques for kernel functions up to hypersingular order had been considered within this thesis. As higher‐order basis functions had been used for the approximation of solution function space and geometry, the results of cBEM in terms of the boundary quantities, the potential and its normal derivative, were of good accuracy. cBEM can be accounted as the foundation of a highly efficient three‐dimensional nonlinear Boundary Element Method solver with possible future application e.g. in the research fields of analyzing nonlinear body motion due to nonlinear wave excitation in numerical wave tanks and for the optimization of ship hull geometries in the early design phase. For offshore operations, the deterministic wave and motion prediction would help to increase safety and cBEM was designed to fit into a holistic approach containing wave inversion, nonlinear wave propagation, and motion prediction. The efficient evaluation of the mixed Boundary Value Problem with highly efficient methods would allow predictions over a period of time that meets industry expectations. The work is structured as follows. In the introduction, the scope of the work is highlighted and limitations and innovations are outlined. In the literature review presented thereafter, the Boundary Element Methods used in Marine Hydrodynamics are categorized into three main streams, and related research contributions are summarized. Based on this, the research gap is outlined and a global hypothesis defined. The research hypotheses structure and summarize the main concerns according to the global hypothesis and give the frame for the development of cBEM. In chapter two, the theory of Boundary Integral Equations and numerical tools accounted for in the Boundary Element Method approach are summarized. Furthermore, the Linear Wave Theory and the High‐Order Spectral method as well as the basic problems of wave‐body interaction are described. On the mathematical foundation and the introduction of the computational methods represented here, the steps for the development of the cBEM solver are presented in chapter three. After an overview of the steps, the Boundary Integral Equations for the different solvers are described. The direct formulation of cBEM is given and the methods accounted for in pre‐, post‐, and processing are introduced. It follows the verification of the approaches including the free surface solver fsBEM, the coupled solver cBEM, and the transient cBEM solver for the continuous and discontinuous surfaces. The validation section, chapter four, shows the application of cBEM for hydrodynamic problems. The submerged and free surface piercing geometries were considered and linear problems with a forced oscillating body, the free surface elevation over a submerged cylinder, and the diffraction of waves due to a body below were compared with literature references. The final discussion in the review of the research hypotheses follows and the conclusions are drawn. By identifying the status of the work described herein, future steps are pointed out. The extension of cBEM to a three‐dimensional solver, equipped with efficient solving strategies and nonlinear extensions is outlined and future applications are given. Their potential is highlighted and the required developments are depicted.