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A two-phase shallow debris flow model with energy balance

Opened Access A two-phase shallow debris flow model with energy balance


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Autor: Bouchut, F.
Fernández-Nieto, Enrique D.
Mangeney, A.
Narbona-Reina, Gladys
Departamento: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Fecha: 2015
Publicado en: ESAIM: Mathematical Modelling And Numerical Analysis, 49, 101-140
Tipo de documento: Artículo
Resumen: This paper proposes a thin layer depth-averaged two-phase model provided by a dissipative energy balance to describe avalanches of solid-fluid mixtures. This model is derived from a 3D two-phase model based on the equations proposed by Jackson [The Dynamics of Fluidized Particles. Cambridges Monographs on Mechanics (2000)] which takes into account the force of buoyancy and the forces of interaction between the solid and fluid phases. Jackson’s model is based on mass and momentum conservation within the two phases, i.e. two vector and two scalar equations. This system has five unknowns: the solid volume fraction, the solid and fluid pressures and the solid and fluid velocities, i.e. three scalars and two vectors. As a result, an additional equation is necessary to close the system. Surprisingly, this issue is inadequately accounted for in the models that have been developed on the basis of Jackson’s work. In particular, Pitman and Le [Philos. Trans. R. Soc. A 363 (2005) 799–819] replac...
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