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Exposés à venir :

18 mai 2022
Elias Drach (LAMA, Université Gustave Eiffel)
A well-balanced entropy scheme for a shallow water type system describing two-phase debris flows
In the context of modeling two-phase debris flows involving a layer of fluid, and a layer of a mixture between grains and fluid, some shallow water systems arise with internal variables.
Our work focus on such a shallow water system with two internal variables and a topography which adds a nonconservative term.

For numerical purposes, it is desirable to deal with a system where the mathematical entropy (the physical
energy of the system) is convex with respect to the chosen conservative variables including the internal variables.

Then at the numerical level, we can look for a scheme satisfying a semi-discrete entropy inequality.

Moreover a crucial point in modeling debris flows is to well describe the stopping of the flow to assess the
maximum velocity, lifetime and runout extent. This means in particular that the flow should stop when
it is a steady state at rest. This is the so called well-balanced property.

Writing the system with conservative variables for which the energy is convex, we derive a well-balanced
scheme satisfying a semi-discrete entropy inequality.
25 mai 2022
Darryl Ondoua (LJLL)
A valider

2 juin 2022
Charlie Hérent (Université Paris-Est (LIGM))
A valider


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