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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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\textit{S. Aliabadi} et al., Int. J. Numer. Methods Fluids 41, No. 8, 809--822 (2003; Zbl 1107.76344)

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