Séance Séminaire

Séminaire des Doctorant·e·s

Coupling methods of phase resolving coastal wave models

Wave propagation has a central role in beach evolution, sediment transport and the impact that natural and artificial structures have on the environment. Modeling these waves with 3D models gives the most accurate results but it is too complex and costly for real applications, so simpler 2D depth-averaged models are used instead. Among these, the Saint-Venant and Boussinesq equations stand out for their complementary ability to capture wave behavior in different conditions. In the last 15 years, combining these into a “hybrid model” by simply switching between them based on wave conditions has showed great promise. Yet, this approach led to mesh-convergence issues, instabilities and spurious waves that put in question its robustness and reliability. In this presentation I will first introduce new coupling methods that we explored aiming to solve these problems. I will show how these methods present similar issues as the hybrid model, which motivates a deeper study of the properties of the model. Then, I will present a mathematical analysis that shows that the linearized model is indeed well-posed in the sense of Hadamard, and that the oscillations observed in these models, at the PDE level, correspond to artificial reflections whose size depends on the dispersiveness of the waves and media. These results contribute to a better understanding for the development of robust depth-averaged water wave models.