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Parallel finite element simulation of mooring forces on floating objects. (English) Zbl 1107.76344

Summary: The coupling between the equations governing the free-surface flows, the six degrees of freedom non-linear rigid body dynamics, the linear elasticity equations for mesh-moving and the cables has resulted in a fluid-structure interaction technology capable of simulating mooring forces on floating objects. The finite element solution strategy is based on a combination approach derived from fixed-mesh and moving-mesh techniques. Here, the free-surface flow simulations are based on the Navier-Stokes equations written for two incompressible fluids where the impact of one fluid on the other one is extremely small. An interface function with two distinct values is used to locate the position of the free-surface. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian-Eulerian domain. This allows us to handle the motion of the time dependent geometries. Forces and momentums exerted on the floating object by both water and hawsers are calculated and used to update the position of the floating object in time. In the mesh moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The non-linear rigid body dynamics equations are coupled with the governing equations of fluid flow and are solved simultaneously to update the position of the floating object. The numerical examples includes a 3D simulation of water waves impacting on a moored floating box and a model boat and simulation of floating object under water constrained with a cable.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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[1] SPLASH nonlinear and unsteady free-surface analysis code for Grand Prix Yacht racing. The Thirteenth Chesapeake Sailing Yacht Symposium, Annapolis, MD, January, 1997.
[2] Aliabadi, Computer Methods in Applied Mechanics and Engineering 190 pp 243– (2000)
[3] Computation of the Free-Surface Flows Around a Ship Using NS Solver FINFLO. VTT Manufacturing Technology, 1997.
[4] Aliabadi, Computer Methods in Applied Mechanics and Engineering 107 pp 209– (1993)
[5] Hughes, Computer Methods in Applied Mechanics and Engineering 66 pp 339– (1998)
[6] Donea, Computational Mechanics 33 pp 689– (1982)
[7] Farhat, International Journal for Numerical Methods in Fluids 21 pp 807– (1995)
[8] Johnson, Computational Mechanics 23 pp 130– (1999)
[9] Hirt, Journal of Computational Physics 39 pp 201– (1981)
[10] Sussman, Journal of Computational Physics 114 pp 146– (1994)
[11] Level set method. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press: Cambridge, 1996.
[12] Aliabadi, Journal of Future Generation Computer Systems 18 pp 627– (2002)
[13] Aliabadi, Simulation 76 pp 257– (2001)
[14] Application of automatic mesh generation and mesh multiplication techniques to very large scale free-surface flow simulations. Proceeding of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler: British Columbia, Canada, September 2000.
[15] Finite element simulation of hydrodynamics problems using unstructured meshes with more than one billion elements. Proceedings of 8th International Conference on Numerical Grid Generation in Computational Field Simulations, Honolulu, Hawaii, June 2-6, 2002.
[16] Aliabadi, International Journal for Numerical Methods in Fluids 21 pp 783– (1995)
[17] A multi-dimensional upwind scheme with no crosswind diffusion. In Finite Element Methods for Convection Dominated Flows, (ed.) AMD-Vol. 34, 19-35 ASME: New York, 1979.
[18] Parallel finite element computations in aerospace applications. Ph.D. Thesis, Department of Aerospace Engineering and Mechanics, University of Minnesota, June 1994.
[19] Gruttmann, International Journal for Numerical Methods in Engineering 35 pp 1111– (1992)
[20] Saad, SIAM Journal of Scientific and Statistical Computing 7 pp 856– (1986)
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