Modelling and simulation of a wave energy converter

Bocchi, Edoardo; He, Jiao; Vergara-Hermosilla, Gastón

doi:10.1051/proc/202107005

Cited by 9 publications

(10 citation statements)

References 10 publications

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“…In a similar way and motivated for mathematical modeling and simulations of a specific type of wave energy converting device, the so-called oscillating water column (OWC) device, Bocchi, He and Vergara-Hermosilla discuss in [1] about the fluid-structure interaction of the partially submerged fixed wall structure of the OWC device, considering the nonlinear shallow water equations to describe the fluid movement, and obtain explicit transmission conditions for the system and respective reduced transmission problems. Recently, Bocchi, He and Vergara-Hermosilla propose in [2] a new and general approach on the mathematical modelling of the OWC, where include the presence of the time-dependent air pressure in the device and prove a local well-posedness result in a Sobolev setting.…”

Section: Contextmentioning

confidence: 99%

“…Recently, Bocchi, He and Vergara-Hermosilla propose in [2] a new and general approach on the mathematical modelling of the OWC, where include the presence of the time-dependent air pressure in the device and prove a local well-posedness result in a Sobolev setting. Hence, by considering their results, in this work we deep on a particular kind of boundary controllability on the transmission problems studied in [1] on an equivalent physical configuration. More precisely, we deal with the exact boundary controllability of nodal profile on a system modelling a structure partially immersed in a fluid governed by the nonlinear shallow water equations [7], considering a discontinuity in the height of the fluid bottom and the transmission conditions developed in [1].…”

Section: Contextmentioning

confidence: 99%

“…Hence, by considering their results, in this work we deep on a particular kind of boundary controllability on the transmission problems studied in [1] on an equivalent physical configuration. More precisely, we deal with the exact boundary controllability of nodal profile on a system modelling a structure partially immersed in a fluid governed by the nonlinear shallow water equations [7], considering a discontinuity in the height of the fluid bottom and the transmission conditions developed in [1]. This physical situation is presented in a graphical sketch in Figure 1.…”

Section: Contextmentioning

confidence: 99%

See 2 more Smart Citations

Boundary controllability of a system modelling a partially immersed obstacle

2021

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In this paper, we address the problem of boundary controllability for the one-dimensional nonlinear shallow water system, describing the free surface flow of water as well as the flow under a fixed gate structure. The system of differential equations considered can be interpreted as a simplified model of a particular type of wave energy device converter called oscillating water column. The physical requirements naturally lead to the problem of exact controllability in a prescribed region. In particular, we use the concept of nodal profile controllability in which at a given point (the node) time-dependent profiles for the states are required to be reachable by boundary controls. By rewriting the system into a hyperbolic system with nonlocal boundary conditions, we at first establish the existence and uniqueness of the semi-global classical solution for the system, then get the local controllability and that of nodal profile using a constructive method. In addition, based on this constructive process, we provide an algorithmic concept to calculate the required boundary control function for generating a solution for solving this control problem.

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Section: Contextmentioning

confidence: 99%

Section: Contextmentioning

confidence: 99%

Section: Contextmentioning

confidence: 99%

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Boundary controllability of a system modelling a partially immersed obstacle

2021

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“…In [34] the same situation was considered with d D 1 in the presence of viscosity. This approach has also been used to model a wave energy converter named the oscillating water column in [7]. These references deal with the exact nonlinear shallow-water equations with a constraint accounting for the presence of the floating body; it can be interesting, especially for numerical simulations, to relax this constraint and use techniques similar to those used to study low-Mach regimes in gases; this is the approach followed in [16,17].…”

Section: Introduction 1general Settingmentioning

confidence: 99%

Freely floating objects on a fluid governed by the Boussinesq equations

Beck

Lannes

2022

Ann. Inst. H. Poincaré C Anal. Non Linéaire

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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 nondispersive 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 interest of its own and for which we consequently provide a general analysis.

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“…In [33] the same situation was considered with d = 1 in the presence of viscosity. This approach has also been used to model a wave energy convertor named the oscillating water column in [7]. These references deal with the exact nonlinear shallow water equations with a constraint accounting for the presence of the floating body; it can be interesting, especially for numerical simulations, to relax this constraint and use techniques similar to those used to study low-Mach regimes in gases; this is the approach followed in [15,16].…”

mentioning

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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Modelling and simulation of a wave energy converter

Cited by 9 publications

References 10 publications

Boundary controllability of a system modelling a partially immersed obstacle

Boundary controllability of a system modelling a partially immersed obstacle

Freely floating objects on a fluid governed by the Boussinesq equations

Freely floating objects on a fluid governed by the Boussinesq equations

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