PhD: MODIFIED ISPH METHOD FOR MODELING THE WAVES INTERACTION WITH THE COASTAL PROTECTION STRUCTURES

Building on Ramos Ortega et al.'s work (2020 and 2022), the initial two years of the PhD thesis will focus on ISPH modifications to improve the numerical simulation of the free surface during wave-defense structure interactions. The approach focuses on particle distribution within the computational domain, particularly around the free surface. Particle distribution is kept uniform through remeshing techniques that redistribute particles on a grid using a "remeshing kernel." This kernel provides remeshing weights based on particle-to-grid point distance while conserving discrete moments (Cottet et al., 2014). Remeshing technique accuracy depends on kernel selection, considering support size, regularity, and moments conservation. An initial comparison of different kernels will be conducted to identify the most suitable for wave-defense structure interactions. Subsequently, Cottet et al.'s (2014) kernel construction methodology will be utilized to create a new kernel designed for free surface treatment. Additionally, the "directional strategy" (Mimeau et al., 2021) will be implemented to reduce algorithmic complexity and overall computational cost by performing advection and remeshing direction by direction. Lastly, addressing numerical diffusion induced by remeshing techniques, which affects ISPH's low-diffusivity properties, will involve applying an anti-diffusion technique via a correction based on the Laplacian of the projected quantity multiplied by an estimated coefficient (Beaudoin et al., 2003).

The modified ISPH will be tested through two benchmarks. The first benchmark involves dam break, allowing for the evaluation of the modified ISPH's ability to simulate the impact of a water sheet on a wall, a problem with significant deformations of the free surface. The benchmark is based on the classical experiment by Lobovsky et al. (2014). In this PhD thesis, experimental data will be provided by the research group IVS, conducting a similar experiment to Lobovsky et al., but focusing on defense structures (see Fig. 4 on the left). The second benchmark will rely on the doctoral work of (Milesi, 2019) at Ecole Centrale Marseille. A sloshing test in a tank filled with water, with a bottom covered by a porous material on a hexapod, was conducted to study the damping of sloshing induced by the porous material (see Fig. 4 on the right). The comparison between experimental and numerical results will validate the modified ISPH and its coupling with the penalization method. 

The last year of the PhD thesis will be dedicated to an applied study of submersion in the Nouvelle Aquitaine region. Two types of submersions can be identified along the coastline of Nouvelle Aquitaine with a North/South division. In the North, submersion is caused by atmospheric surge (i.e. increase in sea level due to pressure drop) combined with swell (i.e. rippling motion agitating the sea without breaking waves). In these areas, submersion has significant ecological consequences in areas where biodiversity protection is crucial. On the other hand, submersion in the South of Nouvelle Aquitaine results more from breaking waves that impact and violently pass over protection structures, potentially leading to severe socio-economic consequences and population displacements. The choice of one or two workshop sites, characterized respectively by swell or breaking waves phenomena, will be guided by discussions with the physical and sociological research groups involved in the CORALI project.

Candidates must hold an engineering degree or a research master's degree in scientific computing and/or numerical fluid mechanics. Candidates are expected to have skills in computer programming (experience in high-performance computing would be highly appreciated) as well as in numerical analysis, particularly a good understanding of numerical methods and schemes for fluid mechanics.