In this work, a new comprehensive method has been developed which enables the solution of large, non-linear motions of rigid bodies in a fluid with a free surface. The application of the modern Eulerian–Lagrangian approach has been translated into an implicit time-integration formulation, a development which enables the use of larger time steps (where accuracy requirements allow it). Novel features of this project include: (1) an implicit formulation of the rigid-body motion in a fluid with a free surface valid for both two or three dimensions and several moving bodies; (2) a complete formulation and solution of the initial conditions; (3) a fully consistent (exact) linearization for free surface flows valid for any boundary elements such that optimal convergence properties are obtained when using a Newton–Raphson solver. The proposed framework has been completed with details on implementation issues referring mainly to the computation of the complete initial conditions and the consistent linearization of the formulation for free surface flows.

The second part of the paper demonstrates the mathematical and numerical formulation through numerical results simulating large free surface flows and non-linear fluid structure interaction. The implicit formulation using a fully consistent linearization based on the boundary element method and the generalized trapezoidal rule has been applied to the solution of free surface flows for the evolution of a triangular wave, the generation of tsunamis and the propagation of a wave up to overturning. Fluid–structure interaction examples include the free and forced motion of a circular cylinder and the sway, heave and roll motion of a U-shaped body in a tank with a flap wave generator. The presented examples demonstrate the applicability and performance of the implicit scheme with consistent linearization. Copyright © 2001 John Wiley & Sons. Ltd.

An implicit boundary element solution with consistent linearization for free surface flows and non‐linear fluid–structure interaction of floating bodies

Computer aided analysis of fluid-structure interaction in ocean engineering problems requires efficient and reliable numerical methods Due to free surface flow and gravity waves they have to consider: large and arbitrary shaped domains, free and moving surfaces, i e nonlinear and time-dependent boundary conditions Assuming a two-dimensional potential flow, the direct boundary element formulation (BEM) is the most efficient solution method Compared to other discretization methods it has minimum discretization expenses, a better representation of complex boundary geometries, and a simple approach to moving boundaries This is achieved by coupling the BEM with a timestepping procedure For numerical simulation of time-dependent, nonlinear (overturning) gravity waves this approach, introduced by Longuet-Higgins and Cokelet [10], now is an optimized and reliable method in use, [6, 7,12, 14] Recently even a three-dimensional wave analysis is proposed: [1, 3, 15, 20] The extension of this BEM time-stepping approach to wave-structure interaction is reasonable, [19], especially to wave channel simulations, [6, 18] A direct BEM formulation allows for different kind of boundary conditions on each finite boundary element Hence, this proposal pay regard to a wide range of different wave-structure interaction problems, ref Fig 11

On the Use of a BEM Time-Stepping Procedure for Nonlinear and Unsteady Wave-Structure Interaction

This paper presents the authors main results of the BEM time-stepping analysis of free surface flow and wave structure interaction in ocean engineering problems and ship hydrodynamics. Starting with propagating and breaking of nonlinear waves some energy and stability criteria are discussed. The influence of space- and time-discretization is given by wave tank simulations. The comparison of BEM computations with measurements shows a most reliable CFL stability criterion, which allows a simple time-step control. Then two typical examples of the so-called 2|-D approach are shown in detail and compared to FEM results: The development of plunging breakers in front of a moving ship and the generation of bow waves.

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BEM Application To Nonlinear Free Surface FlowProblems In Ocean Engineering

A monolithic, ALE finite-element-based strategy for partially submerged solids in an incompressible fluid flow using the mortar method

The paper presents the formulation of a numerical wave channel (NWC) for the investigation of the dynamics of free floating bodies in nonlinear gravity waves. A boundary element (BE) approach for two-dimensional configurations is introduced using cubic spline approximations for the free surface discretization and a double node concept for the modeling of contact points between structures and the fluid. The unknown time-dependent and nonlinear boundary conditions on the free surface are evaluated by a timestepping procedure. In addition, this initial value problem is applicable to the equations of motion of free floating bodies. In this case the right hand sides are the external forces, calculated by integrating the pressure distribution on the submerged surfaces at every time step. Here, the unknown time derivatives of the velocity potential of the fluid have to be derived e.g. by a finite difference scheme or, as proposed here, by a polynomial approximation. The advantages of this procedure are minimal discretization expenses for typical test configurations and a time domain solution, taking into account the fully nonlinear boundary conditions. Several applications of this approach are presented and discussed.

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Mahrenholtz

Papers

The Interaction Of Nonlinear Gravity Waves With Fixed And Floating Structures