Congested shallow water model: on floating body

Godlewski, Edwige; Parisot, Martin; Sainte-Marie, Jacques; Wahl, Fabien

doi:10.5802/smai-jcm.67

Cited by 7 publications

(6 citation statements)

References 31 publications

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“…Let us also mention the connections between (4) and models for wave-structure interactions developed in the very recent years by Lannes [21] and Godlewski et al [17,18], on the basis of the shallow water equations with κ = g/2 > 0, γ = 2 in (4). In wave-structure interaction models, a constraint similar to (4c) can be indeed introduced to model the two possible states of the flow, which is pressurized in the 'interior' domain where the fluid is in contact with the above structure (the height being then constrained by the structure, a floating object or a roof ), and a free surface flow in the 'exterior' domain.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Soft congestion approximation to the one-dimensional constrained Euler equations

Bianchini¹,

Perrin

2021

Nonlinearity

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This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. We provide a detailed description of the effect of the singular pressure on the breakdown of the smooth solutions. Moreover, we rigorously justify the singular limit for smooth solutions towards the free-congested Euler equations, where the compressible (free) dynamics is coupled with the incompressible one in the constrained (i.e. congested) domain.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Soft congestion approximation to the one-dimensional constrained Euler equations

Bianchini¹,

Perrin

2021

Nonlinearity

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“…Wahl [148] and Godlewski et al [147] derive a shallow water model, for applications with a structure at the free surface, by including a supplementary congestion constraint to the equations. To account for freely floating objects, a coupling is introduced between the congested shallow water model and Newton's second law of motion for the body.…”

Section: Congested Shallow Watermentioning

confidence: 99%

Efficient Nonlinear Hydrodynamic Models for Wave Energy Converter Design—A Scoping Study

Davidson

Costello²

2020

JMSE

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This review focuses on the most suitable form of hydrodynamic modeling for the next generation wave energy converter (WEC) design tools. To design and optimize a WEC, it is estimated that several million hours of operation must be simulated, perhaps one million hours of WEC simulation per year of the R&D program. This level of coverage is possible with linear potential flow (LPF) models, but the fidelity of the physics included is not adequate. Conversely, while Reynolds averaged Navier–Stokes (RANS) type computational fluid dynamics (CFD) solvers provide a high fidelity representation of the physics, the increased computational burden of these models renders the required amount of simulations infeasible. To scope the fast, high fidelity options, the present literature review aims to focus on what CFD theories exist intermediate to LPF and RANS as well as other modeling options that are computationally fast while retaining higher fidelity than LPF.

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“…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 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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Congested shallow water model: on floating body

Cited by 7 publications

References 31 publications

Soft congestion approximation to the one-dimensional constrained Euler equations

Soft congestion approximation to the one-dimensional constrained Euler equations

Efficient Nonlinear Hydrodynamic Models for Wave Energy Converter Design—A Scoping Study

Freely floating objects on a fluid governed by the Boussinesq equations

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