Benney's equations: Multi-layer approximations.
Boniface Nkonga (Univ. Cote d’Azur, JAD, CNRS, INRIA Sophia-Antipolis)
| Speaker |
Boniface Nkonga (Univ. Cote d’Azur, JAD, CNRS, INRIA Sophia-Antipolis)
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|---|---|
| When |
Sep 01, 2025
from 11:00 AM to 12:00 PM |
| Where | LH-006, Ground Floor |
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SEMINAR TALK
Abstract: Benney's equations express the dynamics of free surface flow in an incompressible hydrostatic regime. These equations can simulate phenomena such as dam failures, flood development, and flooding. As part of the ITER project, we have derived an extended version of Benney's equations for the flow of liquid metal films designed to protect the walls of magnetic fusion machines. This extension takes into account the presence of an intense magnetic field and a current flowing in the liquid metal.
Fusion plasma activity is subject to instabilities that release large fluxes of electrons, neutrons, alpha particles, and heat (thermal and radiative) to the outside of the plasma confinement. The nuclear blanket protects the (superconducting) coils in particular from the harmful effects that plasma activity could cause.
The circulation of a liquid metal facing the plasma offers an alternative to the most demanding protection challenges. They can withstand heat fluxes without severe damage and open up the possibility of entirely new magnetic fusion operating regimes. Innovative technologies are needed to realize the potential of the fusion process. Liquid lithium surfaces are an innovation that could hold the promise of fusion energy in electricity generation. The presence of free surfaces leads to a problem in a domain with a moving boundary. We consider the 2D context, where the domain has a horizontal main flow direction and a vertical depth direction. The free surface is an unknown of the problem, and we assume the bed dynamics are given. Based on a change of variable that leads to a problem posed in a fixed domain, we will show how different models can be easily derived. We will pay more attention to the Multilayer approximations proposed in [1].
[1] Audusse et al. A multilayer Saint–Venant system with mass exchanges for shallow water flows. Derivation and Numerical Validation.
M2AN Mathematical Modelling and Numerical Analysis, 45 (2011)