Shallow Water models for viscoplastic flows
Résumé
This was one of the plenary talks of the 10th Meeting on Numerical Analysis of PDEs in Chile. In this talk, we provided an overview of some yield stress fluid models in the context of geophysical simulations. As a case study, we described recent events (La Bérarde 2024. Blatten 2025.). We briefly described various types of debris flows and avalanches. Then, we focused specifically on viscoplastic flows. A first approach was presented, based on a monolayer + variational inequality model. Recent results from the PhDs of C. Ginot and M. Wallon were presented, showing a comparison between new experimental configurations and simulations for 3D dambreaks. A second approach was then motivated and presented, based on a shallow multilayer method. It was compared with the 1D experiments of Ancey's group. The mathematical description of discretizations relevant to such models was outlined. Finally, perspectives and future work required were outlined.