DEPARTAMENTO DE ECUACIONES DIFERENCIALES
Y ANÁLISIS NUMÉRICO

UNIVERSIDAD DE SEVILLA
Seminario del Departamento de
Ecuaciones Diferenciales y Análisis Numérico
Fecha : 2 de febrero de 2011
Hora  : 12:00
Lugar : Seminario del Departamento (Fac. de Matemáticas, 3a. planta, módulo 34)
François Bouchut
(CNRS & LAMA Universitéé Paris-Est Marne-la-Vallée, París, Francia)
An entropy satisfying well-balanced solver for the 2d shallow water Savage-Hutter system with curvature terms
Resumen
The Savage-Hutter model describes the evolution of gravity driven shallow flows of granular materials over a general topography. It involves complex curvature force terms that take into account the geometry of the terrain. The model has an energy inequality, and includes non trivial steady states at rest balancing the gravity and the friction force. I shall present a finite volume method for solving the Savage-Hutter model which is based on a Riemann solver with an hydrostatic reconstruction procedure including the curvature terms. It is based on the analysis of trajectories of free particles traveling over the topography. The solver rigorously satisfies the energy inequality, has the well-balanced property with respect to steady states at rest, and is positivity preserving including the case of drying.