Accueil

A Roe-type scheme for two-phase shallow granular flows over variable topography

The paper treats a rather complex geophysical flow which consists of two-phase flow model for gravity-driven mixtures of solid material and fluid. It improves the recent Pitman-Le two-fluid model for debris flow by recovering the conservation of the mixture. The authors introduce a new model expressed in terms of a 4 × 4 hyperbolic system of equations, derive estimates of the four eigenvalues of the new system and analyze the possible breakdown of hyperbolicity. They proceed with the construction, analysis and implementation of a new numerical method for the proposed system. To overcome the difficulties of non-conservative products and stiff forcing terms, they generalize a Roe-type scheme to deal with nonlinear wave propagation. The resulting scheme is shown to be well-balanced for equilibrium as well as being very robust for moving equilibrium.

Eitan Tadmor,
Associate Editor

A Roe-type scheme for two-phase shallow granular flows over variable topography
Marica Pelanti, François Bouchut and Anne Mangeney
ESAIM: M2AN 42 (2008) 851-885
DOI: http://dx.doi.org/10.1051/m2an:2008029