A 3D parallel boundary element method on unstructured triangular grids for fully nonlinear wave-body interactions

Dombre, Emmanuel; Harris, Jeffrey C.; Benoît, Michel; Violeau, Damien; Peyrard, Christophe

doi:10.1016/j.oceaneng.2018.09.044

Cited by 16 publications

(7 citation statements)

References 35 publications

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“…In this respect, recent improvements in the corresponding 2D-NWT of Grilli et al 1,2 by Guerber et al 53 and Dombre et al, 60 concerning floating bodies, are being implemented in this 3D-NWT. Some results are reported in Dombre et al 62 Also, given the physical limitations to what can be modeled with an inviscid NWT, it is logical to consider the possibility of coupling this NWT to a viscous model for flow around a body. We have shown in earlier work 56 that obtaining the internal velocity quickly using the FMM is straightforward.…”

Section: Discussionmentioning

confidence: 99%

“…As for many applications it is not necessary to consider very long simulation times, the advantages of using a symplectic integrator may not be immediately apparent. In work in progress, the 3D-NWT was extended to more complex surface-piercing support structures used in offshore engineering 57 .…”

Section: Time Integration In the Nwtmentioning

confidence: 99%

“…In work in progress, the 3D-NWT was extended to more complex surface-piercing support structures used in offshore engineering. 62…”

Section: Time Integration In the Nwtmentioning

confidence: 99%

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Nonlinear time‐domain wave‐structure interaction: A parallel fast integral equation approach

Harris

Dombre

Benoît

et al. 2021

Numerical Methods in Fluids

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We report on the development and validation of a new Numerical Wave Tank (NWT) solving fully nonlinear potential flow (FNPF) equations, as a more efficient variation of Grilli et al.'s NWT [Grilli et al., A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom, International Journal for Numerical Methods in Fluids 35 ( 2001) 829-867], which was successful at modeling many wave phenomena, including landslide-generated tsunamis, rogue waves, and the initiation of wave breaking over slopes. This earlier NWT combined a three dimensional MII (mid-interval interpolation) boundary element method (BEM) to an explicit mixed Eulerian-Lagrangian time integration. The latter was based on second-order Taylor series expansions for the mesh geometry and Dirichlet free surface boundary condition for the potential, requiring high-order derivatives to be computed in space and time. Here, to be able to solve large scale wave-structure interaction problems for surface-piercing bodies of complex geometry, of interest for ocean engineering and naval hydrodynamics applications, the NWT is reformulated to use cubic Bspline meshes and the BEM solution is accelerated with a parallelized Fast Multipole Method (FMM) based on ExaFMM, one of the fastest open source FMM to date. The NWT accuracy, convergence, and scaling are first assessed for simple cases, by comparing results with those of the earlier MII-NWT as a function of mesh size and other model parameters. The relevance of the new NWT for solving the targeted applications is then demonstrated for surface piercing fixed cylinders, for which we show that results agree well with theoretical and experimental data for wave elevation and hydrodynamic forces.

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Section: Discussionmentioning

confidence: 99%

Section: Time Integration In the Nwtmentioning

confidence: 99%

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Nonlinear time‐domain wave‐structure interaction: A parallel fast integral equation approach

Harris

Dombre

Benoît

et al. 2021

Numerical Methods in Fluids

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“…For an overview of work on the BEM methods up to the end of the 20 th century, the reader is referred to Kim et al (1999). More recently, Guerber et al (2012) and Dombre et al (2019) presented in great detail and implemented a complete NWT, in 2D and 3D respectively. Note that with the BEM schemes, a special attention must be given to the treatment of sharp corners (Hague and Swan, 2009).…”

Section: Introduction and Scope Of The Studymentioning

confidence: 99%

Development and validation of a numerical wave tank based on the Harmonic Polynomial Cell and Immersed Boundary methods to model nonlinear wave-structure interaction

Robaux

Benoît

2021

Journal of Computational Physics

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A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method (IBM) for capturing the free surface motion. This NWT can consider fixed, submerged or wall-sided surface piercing, bodies. To compute the flow around the body and associated pressure field, a novel multi overlapping grid method is implemented. Each grid having its own free surface, a two-way communication is ensured between the problem in the body vicinity and the larger scale wave propagation problem. Pressure field and nonlinear loads on the structure are computed by solving a boundary value problem on the time derivative of the potential. The stability and convergence properties of the solver are studied basing on extensive tests with standing waves of large to extreme wave steepness, up to H/λ = 0.2 (H is the crest-to-trough wave height and λ the wavelength). Ranges of optimal time and spatial discretizations are determined and high-order convergence properties are verified, first without using any filter. For cases with either high level of nonlinearity or long simulation duration, the use of mild Savitzky-Golay filters is shown to extend the range of applicability of the model. Then, the NWT is tested against two wave flume experiments, analyzing forces on bodies in various wave conditions. First, nonlinear components of the vertical force acting on a small horizontal circular cylinder with low submergence below the mean water level are shown to be accurately simulated up to the third order in wave steepness. The second case is a dedicated experiment with a floating barge of rectangular cross-section. This very challenging case (body with sharp corners in large waves) allows to examine the behavior of the model in situations at and beyond the limits of its formal application domain. Though effects associated with viscosity and flow separation manifest experimentally, the NWT proves able to capture the main features of the wave-structure interaction and associated loads.

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“…Early studies considered infinitesimal motions and focused mainly on the stability of the equilibrium of floating bodies [2,20] and engineers use a phenomenological linear integro-differential equation, the so-called Cummins equations [11,30] to describe the motion of the floating object. In these linear models, the pressure P i exerted by the fluid on the object is given by the (linear approximation of the) Bernoulli equation, The above formulation of the problem of waves interacting with a floating body can easily be extended to the nonlinear case (see for instance [42] where Zakharov's Hamiltonian formulation of the water waves problem is extended in the presence of a floating object or, for instance [38,12] for numerical studies). We do not provide too many details here because we shall rather use the approach of [26] in which the pressure P i exerted by the fluid on the object is understood as the Lagrange multiplier associated to the constraint that, under the object, the surface of the fluid coincides with the bottom of the object.…”

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confidence: 99%

Freely floating objects on a fluid governed by the Boussinesq equations

Beck¹,

Lannes²

2021

Preprint

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We investigate here the interactions of waves governed by a Boussinesq system with a partially immersed body allowed to move freely in the vertical direction. We show that the whole system of equations can be reduced to a transmission problem for the Boussinesq equations with transmission conditions given in terms of the vertical displacement of the object and of the average horizontal discharge beneath it; these two quantities are in turn determined by two nonlinear ODEs with forcing terms coming from the exterior wave-field. Understanding the dispersive contribution to the added mass phenomenon allows us to solve these equations, and a new dispersive hidden regularity effect is used to derive uniform estimates with respect to the dispersive parameter. We then derive an abstract general Cummins equation describing the motion of the solid in the return to equilibrium problem and show that it takes an explicit simple form in two cases, namely, the nonlinear non dispersive and the linear dispersive cases; we show in particular that the decay rate towards equilibrium is much smaller in the presence of dispersion. The latter situation also involves an initial boundary value problem for a nonlocal scalar equation that has an interest of its own and for which we consequently provide a general analysis. G. B. was supported by the Del Duca fondation. D. L is partially supported by the ANR-18-CE40-0027 Singflows, the ANR-17-CE40-0025 NABUCO and the Del Duca fondation.

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A 3D parallel boundary element method on unstructured triangular grids for fully nonlinear wave-body interactions

Cited by 16 publications

References 35 publications

Nonlinear time‐domain wave‐structure interaction: A parallel fast integral equation approach

Nonlinear time‐domain wave‐structure interaction: A parallel fast integral equation approach

Development and validation of a numerical wave tank based on the Harmonic Polynomial Cell and Immersed Boundary methods to model nonlinear wave-structure interaction

Freely floating objects on a fluid governed by the Boussinesq equations

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