Numerical Simulations of the Interaction of Solitary Waves and Elastic Structures with a Fully Eulerian Method
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Numerical Simulations of the Interaction of Solitary Waves and Elastic Structures with a Fully Eulerian Method Julien Deborde1 · Thomas Milcent1,2 · Pierre Lubin1 · Stéphane Glockner1 Received: 28 August 2019 / Accepted: 20 April 2020 © Springer Nature Switzerland AG 2020
Abstract Wave attenuation by elastic structures is a challenging issue when studying shoreline protection subjected to waves and erosion. For this purpose, a fully Eulerian method is then developed to solve the problem of fluid–elastic structure interactions for incompressible flows. The specificity of the proposed approach is to use a combination of a reinitialization technique for the interface and linear extrapolations for the deformations to prevent numerical instabilities for the computation of the elastic forces. First, we verify and validate our approach on several test cases. Next, we apply this method to illustrate the capacity of the model to study the wave damping phenomenon by a single or several elastic structures. Keywords Fluid–structure interaction · Eulerian elasticity · Finite volume · Navier–Stokes equations · Coastal wave attenuation
1 Introduction The interaction between a fluid and an elastic solid is a very challenging problem with a wide range of applications (biomechanics, medicine, environmental issues, etc.). When
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s42286020-00037-7) contains supplementary material, which is available to authorized users.
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Thomas Milcent [email protected] Julien Deborde [email protected] Pierre Lubin [email protected] Stéphane Glockner [email protected]
1
Univ. Bordeaux, I2M, UMR 5295, 33400 Talence, France
2
Arts et Métiers Paristech, 33607 Pessac, France
J. Deborde et al.
studying protection of shorelines subjected to waves, hard engineering techniques are often used to protect coastal shores (sea walls, groynes, gabions, and rock armours). However, the interaction between flexible plants and the free surface of waves can also be investigated to design a more ecological solution to protect the shoreline. Indeed, it has been shown that waves can be damped due to the presence of seagrass [1,17,29]. Several experiments have been conducted to reproduce the attenuation process and to identify the physical characteristics of the vegetation responsible for an optimal protection. Posidoniae and mangroves have been tested [21,22,24,29,31], indicating that vegetation density, height, thickness, submersion, and surface covered by the plants were key factors. Flexibility is also an important factor to take into account if the capacity of the submerged plants to protect the shoreline has to be evaluated [33]. Experimental studies are now complemented by numerical simulations to investigate waves and vegetation interaction [33], and tsunamis and cylindrical rigid structures [34,42,44] compared to experimental data [20]. However, interactions between waves and submerged artificial elastic structures ar
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