The derivation of a discrete mooring model for floating structures is presented in this paper. The method predicts the steady-state solution for the shape of an elastic cable and the tension forces under consideration of static loads. It is based on a discretization of the cable in mass points connected with straight but elastic bars. The successive approximation is applied to the resulting system of equations which leads to a significant reduction of the matrix size in comparison to the matrix of a Newton–Raphson method. The mooring model is implemented in the open-source computational fluid dynamics (CFD) model REEF3D. The solver has been used to study various problems in the field of wave hydrodynamics and fluid–structure interaction. It includes floating structures through a level set function and captures its motion using Newton and Euler equations in six degrees-of-freedom (6DOF). The fluid–structure interaction is solved explicitly using an immersed boundary method based on the ghost cell method. The applications show the accuracy of the solver and the effects of mooring on the motion of floating structures.
Issue Section:
CFD and VIV
References
1.
Davidson
, J.
, and Ringwood
, J.
, 2017
, “Mathematical Modelling of Mooring Systems for Wave Energy Converters—A Review
,” Energies
, 10
(5
), p. 666
. 2.
Huang
, S.
, 1994
, “Dynamic Analysis of Three-Dimensional Marine Cables
,” Ocean Eng.
, 21
(6
), pp. 587
–605
. 3.
Aamo
, O. M.
, and Fossen
, T. I.
, 2001
, “Finite Element Modelling of Moored Vessels
,” Math. Comput. Modell. Dyn. Syst.
, 7
(1
), pp. 47
–75
. 4.
Palm
, J.
, Eskilsson
, C.
, and Bergdahl
, L.
, 2017
, “An hp-Adaptive Discontinuous Galerkin Method for Modelling Snap Loads in Mooring Cables
,” Ocean Eng.
, 144
(1
), pp. 266
–276
. 5.
Hall
, M.
, and Goupee
, A.
, 2015
, “Validation of a Lumped-Mass Mooring Line Model With DeepCwind Semisubmersible Model Test Data
,” Ocean Eng.
, 104
(1
), pp. 590
–603
. 6.
Leitzke
, H.
, 1983
, “Berechnung von Form und Kräften biegeschlaffer, räumlicher Zugsysteme
,” Ph.D. thesis, University of Rostock
, Rostock
.7.
Hackmann
, W.
, 1983
, “Mathematische Begründung Von Verfahren Zur Berechnung Von Form Und Zugkraft in Fadenzugsystemen
,” ZAMM
, 63
(3
), pp. 173
–184
. 8.
Paschen
, M.
, Niedzwiedz
, G.
, and Winkel
, H.-J.
, 2004
, “Fluid Structure Interactions at Towed Fishing Gears
,” 23rd International Conference on Offshore Mechanics and Arctic Engineering
, Vancouver, Canada
, June 20–25
, pp. 855
–865
.9.
Bihs
, H.
, Kamath
, A.
, Chella
, M. A.
, Aggarwal
, A.
, and Arntsen
, Ø. A.
, 2016
, “A New Level Set Numerical Wave Tank With Improved Density Interpolation for Complex Wave Hydrodynamics
,” Comput. Fluids
, 140
(1
), pp. 191
–208
. 10.
Kamath
, A.
, Chella
, M. A.
, Bihs
, H.
, and Arntsen
, Ø. A.
, 2017
, “Energy Transfer Due to Shoaling and Decomposition of Breaking and Non-Breaking Waves Over a Submerged Bar
,” Eng. Appl. Comput. Fluid Mech.
, 11
(1
), pp. 450
–466
. 11.
Kamath
, A.
, Chella
, M. A.
, Bihs
, H.
, and Arntsen
, Ø. A.
, 2015
, “Evaluating Wave Forces on Groups of Three and Nine Cylinders Using a 3D Numerical Wave Tank
,” Eng. Appl. Comput. Fluid Mech.
, 9
(1
), pp. 343
–354
. 12.
Grotle
, E. L.
, Bihs
, H.
, and Æsøy
, V.
, 2017
, “Experimental and Numerical Investigation of Sloshing Under Roll Excitation at Shallow Liquid Depths
,” Ocean Eng.
, 138
(1
), pp. 73
–85
. 13.
Berthelsen
, P.
, and Faltinsen
, O.
, 2008
, “A Local Directional Ghost Cell Approach for Incompressible Viscous Flow Problems With Irregular Boundaries
,” J. Comput. Phys.
, 227
(9
), pp. 4354
–4397
. 14.
Yang
, J.
, and Balaras
, E.
, 2006
, “An Embedded-Boundary Formulation for Large-Eddy Simulation of Turbulent Flows Interacting With Moving Boundaries
,” J. Comput. Phys.
, 215
(1
), pp. 12
–40
. 15.
Calderer
, A.
, Kang
, S.
, and Sotiropoulos
, F.
, 2014
, “Level Set Immersed Boundary Method for Coupled Simulation of Air/Water Interaction With Complex Floating Structures
,” J. Comput. Phys.
, 277
(1
), pp. 201
–227
. 16.
Yang
, J.
, and Stern
, F.
, 2012
, “A Simple and Efficient Direct Forcing Immersed Boundary Framework for Fluid–Structure Interactions
,” J. Comput. Phys.
, 231
(15
), pp. 5029
–5061
. 17.
Carrica
, P.
, Noack
, R.
, and Stern
, F.
, 2007
, “Ship Motions Using Single-Phase Level Set With Dynamic Overset Grid
,” Comput. Fluids
, 36
(9
), pp. 1415
–1433
. 18.
Bihs
, H.
, and Kamath
, A.
, 2017
, “A Combined Level Set/Ghost Cell Immersed Boundary Representation for Floating Body Simulations
,” Int. J. Numer. Methods Fluids
, 83
(12
), pp. 905
–916
. 19.
Kamath
, A.
, Bihs
, H.
, and Arntsen
, Ø. A.
, 2017
, “Study of Water Impact and Entry of a Free Falling Wedge Using Computational Fluid Dynamics Simulations
,” ASME J. Offshore Mech. Arct. Eng.
, 139
(3
), p. 031802
. 20.
Sussman
, M.
, Smereka
, P.
, and Osher
, S.
, 1994
, “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow
,” J. Comput. Phys.
, 114
(1
), pp. 146
–159
. 21.
Jiang
, G.
, and Shu
, C.
, 1996
, “Efficient Implementation of Weighted ENO Schemes
,” J. Comput. Phys.
, 126
(1
), pp. 202
–228
. 22.
Zhang
, J.
, and Jackson
, T. L.
, 2009
, “A High-Order Incompressible Flow Solver With WENO
,” J. Comput. Phys.
, 228
(7
), pp. 146
–159
. 23.
Chorin
, A. J.
, 1968
, “Numerical Solution of the Navier–Stokes Equations
,” Math. Comput.
, 22
(104
), pp. 745
–762
. 24.
van der Vorst
, H.
, 1992
, “BiCGStab: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
,” SIAM J. Sci. Comput.
, 13
(2
), pp. 631
–644
. 25.
Shu
, C.
, and Osher
, S.
, 1988
, “Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes
,” J. Comput. Phys.
, 77
(2
), pp. 439
–471
. 26.
Osher
, S.
, and Sethian
, J.
, 1988
, “Fronts Propagating With Curvature-Dependent Speed: Algorithms Based on Hamilton–Jacobi Formulations
,” J. Comput. Phys.
, 79
(1
), pp. 12
–49
. 27.
Jiang
, G.
, and Peng
, D.
, 2000
, “Weighted ENO Schemes for Hamilton Jacobi Equations
,” SIAM J. Sci. Comput.
, 21
(6
), pp. 2126
–2143
. 28.
Brackbill
, J.
, Kothe
, D.
, and Zemach
, C.
, 1992
, “A Continuum Method for Modeling Surface Tension
,” J. Comput. Phys.
, 100
(2
), pp. 335
–354
. 29.
Fossen
, T.
, 1994
, Guidance and Control of Ocean Vehicles
, John Wiley & Sons
, Chichester
.30.
Udaykumar
, H.
, Mittal
, R.
, Rampunggoon
, P.
, and Khanna
, A.
, 2001
, “A Sharp Interface Cartesian Grid Method for Simulating Flows With Complex Moving Boundaries
,” J. Comput. Phys.
, 174
(1
), pp. 345
–380
. 31.
Faltinsen
, O.
, 1990
, Sea Loads on Ships and Offshore Structures
, Cambridge University Press
, Cambridge
.32.
Ren
, B.
, He
, M.
, Dong
, P.
, and Wen
, H.
, 2015
, “Nonlinear Simulations of Wave-Induced Motions of a Freely Floating Body Using WCSPH Method
,” Appl. Ocean Res.
, 50
(1
), pp. 1
–12
. Copyright © 2019 by ASME
You do not currently have access to this content.
