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Section: New Results
Analysis of models in Fluid Mechanics
Analysis of the Riemann problem for a shallow water model with two velocities
Participants : Emmanuel Audusse, Edwige Godlewski, Martin Parisot.
In collaboration with N. Aguillon.
The question addressed in [24] is the hyperbolicity of a shallow water model with two velocities. The model is written in a nonconservative form and the analysis of its eigenstructure shows the possibility that two eigenvalues coincide. A definition of the nonconservative product is given which enables us to analyse the resonance and coalescence of waves. Eventually, we prove the well-posedness of the two dimensional Riemann problem with initial condition constant by half-plane.
Different formulations of an elliptic problem issued from geophysics
Participants : Cindy Guichard, Ani Miraçi, Yohan Penel, Jacques Sainte-Marie.
A simplified problem coming from [33] involving pressure and velocity unknowns is studied. Some weak formulations (conform or mixed) are derived and their well-posedness is analysed. These weak formulations are then discretised in a finite element framework with suitable discrete spaces.