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Seminari di Analisi Numerica: The system of shallow water in 2d with topographic curvature and the Shaltop code

25 Luglio 2018 - ore 11.30 aula 2BC/30 - Francois Bouchut

ARGOMENTI: Seminars

Mercoledi' 25 luglio 2018, ore 11:30, aula 2BC/30

Francois Bouchut
-----------------
CNRS & Universita' Paris-Est
77454 Marne-la-Valle' - France

terra' un seminario dal titolo:

The system of shallow water in 2d with topographic curvature
and the Shaltop code


ABSTRACT
I shall describe the modeling of granular flows over a curved 2d
topography by shallow water / Savage-Hutter type models following
Bouchut & Westdickenberg 2004. The thin-layer approximation is obtained
from incompressible Euler equations with friction conditions
at the bottom. The free surface is described by the width of the thin
layer in the direction normal to the bottom. In the thin-layer model
the friction is multivalued when the velocity vanishes, in accordance
with Coulomb friction modeling. The force applied by the flow onto
the terrain is expressed in terms of average quantities, knowing the
asymptotic expansion of the Euler equations.
A numerical finite volume method will be introduced. It uses an
approximate Riemann solver together with reconstructed states, in
the spirit of well-balanced methods, and includes the effect of topography
curvature. The scheme is well-balanced and satisfies a semi-discrete
entropy inequality that ensures its robustness. A code named Shaltop
using these features has been used in several geophysical studies, showing
its ability to deal with real data with rapidly varying topography.