| A Roe-type scheme for two-phase shallow granular flows over variable topography (M. Pelanti et al.) |
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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,
A Roe-type scheme for two-phase shallow granular flows over variable topography
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