近年來，台灣周圍海域之海上結構物已從近岸海岸保護的結構物，發展到離岸式風力發電機的興建，離岸風電的發展已從近岸擴展至更深水的區域。在中間水深或較深水的條件下，風機的設計往往選擇浮動式的設計，故海上的流固交互作用成為重要的議題。

本研究以開放源計算流體力學工具包OpenFOAM®的求解器interDyMFoam為基底，進行求解器的改善，加入固體計算的收斂條件，使其成為緊耦合(tightly coupled)求解器CoupledinterDyMFoam。本文在改善求解器interDyMFoam後，透過新的緊耦合求解器CoupledinterDyMFoam進行流固耦合的計算，其計算包含垂向衰減試驗、單自由度轉動試驗、以及波浪與結構物交互作用試驗。

除了進行流固耦合的模擬，本研究亦作繫繩模型的建立。繫繩模型使用MATLAB®程式語言進行繫繩程式的撰寫，模型使用之數值方法為有限元素法，並利用更新式拉格朗日法作繫繩的描述。繫繩繫繩的位置求解使用Newton-Raphson法位移增量法進行迭代求解，而其運動的描述則使用Newmark’s β法。

The fluid-structure interaction(FSI) model for simulating floating structure with mooring lines is developed in this study. The establishment of the model can be divided into parts of Computational Fluid Dynamics (CFD) model and mooring model. About CFD model part, the open-source CFD toolbox OpenFOAM® version v.1712 is used, and its solver – interDyMFoam is chosen as the base of FSI solver. The criteria and relaxation factor computation procedures are added in interDyMFoam solver to decrease artificial added mass effect, and the new solver is named CoupledinterDyMFoam. Validation of CoupledinterDyMFoam is carried out on a benchmark case of heave decay test, roll decay test, and wave-structure interaction test. The mooring model is established in MATLAB®, its theory is based on finite element method, and it used Newmark’s beta method as a time integration method. The mooring model is validated against benchmark analytical solution of elastic catenary and numerical results from Niewiarowski et al. (2018). The model of floating structure with mooring lines is successfully built by connecting CoupledinterDyMFoam with mooring model.

Bathe, K. J. (2006). Finite element procedures. Klaus-Jurgen Bathe.
Chen, L., Sun, L., Zang, J., Hillis, A. J., & Plummer, A. R. (2016). Numerical study of roll motion of a 2-D floating structure in viscous flow. Journal of Hydrodynamics, 28(4), 544-563.
Chow, J. H., & Ng, E. Y. K. (2016). Strongly coupled partitioned six degree-of-freedom rigid body motion solver with Aitken's dynamic under-relaxation. International Journal of Naval Architecture and Ocean Engineering, 8(4), 320-329.
Davidson, J., & Ringwood, J. (2017). Mathematical modelling of mooring systems for wave Energy converters—A review. Energies, 10(5), 666.
Devolder, B., Schmitt, P., Rauwoens, P., Elsaesser, B., & Troch, P. (2015, September). A Review of the Implicit Motion Solver Algorithm in OpenFOAM® to Simulate a Heaving Buoy. In Proceedings of the 18th Numerical Towing Tank Symposium (pp. 1-6).
Devolder, B., Troch, P., & Rauwoens, P. (2018). Accelerated numerical simulations of a heaving floating body by coupling a motion solver with a two-phase fluid solver. Computers & Mathematics with Applications.
Dunbar, A. J., Craven, B. A., & Paterson, E. G. (2015). Development and validation of a tightly coupled CFD/6-DOF solver for simulating floating offshore wind turbine platforms. Ocean Engineering, 110, 98-105.
Förster, C., Wall, W. A., & Ramm, E. (2007). Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Computer methods in applied mechanics and engineering, 196(7), 1278-1293.
Hou, G., Wang, J., & Layton, A. (2012). Numerical methods for fluid-structure interaction—a review. Communications in Computational Physics, 12(2), 337-377.
Itō, S. (1977). Study of the transient heave oscillation of a floating cylinder , Doctoral dissertation, Massachusetts Institute of Technology,Cambridge,California.
Jung, K. H., Chang, K. A., & Jo, H. J. (2006). Viscous effect on the roll motion of a rectangular structure. Journal of engineering mechanics, 132(2), 190-200.
Küttler, U., & Wall, W. A. (2008). Fixed-point fluid–structure interaction solvers with dynamic relaxation. Computational Mechanics, 43(1), 61-72.
Luongo, A., & Zulli, D. (2013). Mathematical models of beams and cables. John Wiley & Sons.
Maskell, S. J., & Ursell, F. (1970). The transient motion of a floating body. Journal of Fluid Mechanics, 44(2), 303-313.
Niewiarowski, A., Adriaenssens, S., Pauletti, R. M., Addi, K., & Deike, L. (2018). Modeling underwater cable structures subject to breaking waves. Ocean Engineering, 164, 199-211.
Open CFD, 2018, OpenFOAM user guide. OpenFOAM Foundation
Palm, J. (2012). Connecting OpenFOAM with matlab. Online: http://www. tfd. chalmers. se/hani/kurser/OS CFD, 2012.
Palm, J., Eskilsson, C., Paredes, G. M., & Bergdahl, L. (2016). Coupled mooring analysis for floating wave energy converters using CFD: Formulation and validation. International Journal of Marine Energy, 16, 83-99.
Papini, D. A. N. I. E. L. (2010). On shape control of cables under vertical static loads. M. S. thesis, Lund University, Lund.
Pomeranz, S. B. (2017). Aitken’s Δ2 method extended. Cogent Mathematics & Statistics, 4(1), 1308622.
Ransley, E. J., Greaves, D., Raby, A., Simmonds, D., & Hann, M. (2017). Survivability of wave energy converters using CFD. Renewable Energy, 109, 235-247.
Ursell, F. (1949). On the heaving motion of a circular cylinder on the surface of a fluid. The Quarterly Journal of Mechanics and Applied Mathematics, 2(2), 218-231.
Ursell, F. (1964). The decay of the free motion of a floating body. Journal of Fluid Mechanics, 19(2), 305-319.
van Daalen, E. F. G. (1994). Numerical and theoretical studies of water waves and floating bodies.
Van Loon, R., Anderson, P. D., Van de Vosse, F. N., & Sherwin, S. J. (2007). Comparison of various fluid–structure interaction methods for deformable bodies. Computers & structures, 85(11-14), 833-843.
Yeung, R. W. (1982). The transient heaving motion of floating eylinders. Journal of engineering mathematics, 16(2), 97-119.
Yvin, C., Leroyer, A., Visonneau, M., & Queutey, P. (2018). Added mass evaluation with a finite-volume solver for applications in fluid–structure interaction problems solved with co-simulation. Journal of Fluids and Structures, 81, 528-546.