Features and References ======================= .. _theory: Most of MoorDyn’s theory is described in the following publications. This page gives a very high-level overview, highlights specific theory aspects that may be important to users, and lists the papers where more detail can be found. Features -------- Version 1 ^^^^^^^^^ MoorDyn is based on a lumped-mass discretization of a mooring line’s dynamics, and adds point-mass and rigid-body objects to enable simulation of a wide variety of mooring and cabling arrangements. Hydrodynamics are included using a version of the Morison equation. Version 2 ^^^^^^^^^ MoorDyn v2 contains all the features of v1 with the following additional features: - Simulation of 6 degree of freedom objects - Non-linear tension - Wave kinematics - Bending stiffness - Bathymetry - Seabed friction The main difference between MoorDyn-C and MoorDyn-F is that MoorDyn-C uses quaternions to describe the orientation of 6DOF objects, while F uses traditional Euler angles to handle 6DOF object rotations. Orientation of 6 DOF objects: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ MoorDyn-C, MoorDyn-F, and `MoorPy `_ share the same Intrinsic Euler-XYZ (Tait-Bryan) angles criteria to compute orientations. You can learn more about this on `Hall M. Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians. Energies. 2024; 17(13):3155. https://doi.org/10.3390/en17133155 `_ However, while on MoorDyn-F this is handled by considering orientation matrices, on MoorDyn-C quaternions are considered to describe the location and orientation of 6 DOF objects. Further description of quaternions can be found in PR #90 in the MoorDyn repository, put together by Alex Kinley of Kelson Marine: https://github.com/FloatingArrayDesign/MoorDyn/pull/90#issue-1777700494 References ---------- The theory behind MoorDyn is available in a collection of papers, listed below by which version they were implemented in. Version 1 ^^^^^^^^^ The v1 lumped-mass formulation of MoorDyn as well as its validation against experiments: `M. Hall and A. Goupee, “Validation of a lumped-mass mooring line model with DeepCwind semisubmersible model test data,” Ocean Engineering, vol. 104, pp. 590–603, Aug. 2015. `_ Coupling with WEC-Sim or any Simulink code for wave energy converter simulation: `S. Sirnivas, Y.-H. Yu, M. Hall, and B. Bosma, “Coupled Mooring Analysis for the WEC-Sim Wave Energy Converter Design Tool,” in Proceedings of the 35th International Conference on Ocean, Offshore and Arctic Engineering, Busan, South Korea, 2016. `_ `G. Vissio, B. Passione, and M. Hall, “Expanding ISWEC Modelling with a Lumped-Mass Mooring Line Model,” presented at the European Wave and Tidal Energy Conference, Nantes, France, 2015. `_ Version 2 ^^^^^^^^^ Version 2 builds upon the capabilities of Version 1. The theory behind the new features is described in the following references. Early work on seabed friction and independent fairlead points: `M. Hall, “Efficient Modelling of Seabed Friction and Multi-Floater Mooring Systems in MoorDyn,” in Proceedings of the 12th European Wave and Tidal Energy Conference, Cork, Ireland, 2017. `_ Preliminary comparison of seabed friction formulations: `K. Devries, M. Hall, “Comparison of Seabed Friction Formulations in a LumpedMass Mooring Model”. in Proceedings of the ASME International Offshore Wind Technical Conference, San Francisco, California, Nov. 2018. `_ Overview of MoorDyn v2 (bodies, rods, and line failures): `Hall, Matthew, “MoorDyn V2: New Capabilities in Mooring System Components and Load Cases.” In Proceedings of the ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. virtual conference, 2020. `_ Seabed friction and bathymetry approach used in v2: `Housner, Stein, Ericka Lozon, Bruce Martin, Dorian Brefort, and Matthew Hall, “Seabed Bathymetry and Friction Modeling in MoorDyn.” Journal of Physics: Conference Series 2362, no. 1, Nov 2022: 012018. `_ Implementation of bending stiffness modeling for power cables: `Hall, Matthew, Senu Sirnivas, and Yi-Hsiang Yu, “Implementation and Verification of Cable Bending Stiffness in MoorDyn.” In ASME 2021 3rd International Offshore Wind Technical Conference, V001T01A011. Virtual, Online: American Society of Mechanical Engineers, 2021. `_ Non-linear line stiffness: `Lozon, Ericka, Matthew Hall, Paul McEvoy, Seojin Kim, and Bradley Ling, “Design and Analysis of a Floating-Wind Shallow-Water Mooring System Featuring Polymer Springs.” American Society of Mechanical Engineers Digital Collection, 2022. `_ Bladed-MoorDyn Coupling: `Alexandre, Armando, Francesc Fabregas Flavia, Jingyi Yu, Ali Bakhshandehrostami, and Steven Parkinson. "Coupling Bladed With External Finite-Element Mooring Libraries." American Society of Mechanical Engineers Digital Collection, 2023. `_ Viscoelastic approach for non-linear rope behavior: `Hall, Matthew, Brian Duong, and Ericka Lozon, “Streamlined Loads Analysis of Floating Wind Turbines With Fiber Rope Mooring Lines.” In ASME 2023 5th International Offshore Wind Technical Conference, V001T01A029. Exeter, UK: American Society of Mechanical Engineers, 2023. `_ Updated MoorDyn-OpenFOAM Coupling: `Haifei Chen, Tanausú Almeida Medina, and Jose Luis Cercos-Pita, "CFD simulation of multiple moored floating structures using OpenFOAM: An open-access mooring restraints library." Ocean Engineering, vol. 303, Jul. 2024. `_ Reef3D-MoorDyn Coupling: `Soydan, Ahmet, Widar Weizhi Wang, and Hans Bihs. "An Improved Direct Forcing Immersed Boundary Method With Integrated Mooring Algorithm for Floating Offshore Wind Turbines." American Society of Mechanical Engineers Digital Collection, 2024. `_ Modeling of Bi-stable Nonlinear Energy Sinks in MoorDyn (most recent description of MoorDyn theory): `Anargyros Michaloliakos, Wei-Ying Wong, Ryan Davies, Malakonda Reddy Lekkala, Matthew Hall, Lei Zuo, Alexander F. Vakakis, "Stabilizing dynamic subsea power cables using Bi-stable nonlinear energy sinks", Ocean Engineering, vol. 334, August 2025. `_ The Fortran version of MoorDyn is available as a module inside of OpenFAST: https://openfast.readthedocs.io/en/main/ Hydrodynamics of 6DOF objects follows a similar approach to Hydrodyn: https://www.nrel.gov/wind/nwtc/assets/downloads/HydroDyn/HydroDyn_Manual.pdf Quaternion references: 1. Fossen, Thor I. Handbook of marine craft hydrodynamics and motion control. Page 25 John Wiley & Sons, 2011. 2. https://en.wikipedia.org/wiki/Gimbal_lock 3. https://www.ashwinnarayan.com/post/how-to-integrate-quaternions/ 4. https://en.wikipedia.org/wiki/Quaternion#Hamilton_product MoorDyn-C Packages used: - Eigen: https://eigen.tuxfamily.org - Catch2: https://github.com/catchorg/Catch2 - KISSFFT: https://github.com/mborgerding/kissfft