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A Multilayer Shallow Water Approach for Polydisperse Sedimentation with Sediment Compressibility and Mixture Viscosity

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Abstract

A three-dimensional multilayer shallow water approach to study polydisperse sedimentation and sediment transport in a viscous fluid is presented. The fluid is assumed be loaded with finely dispersed solid particles that belong to a finite number of species that differ in density and size. The model formulation allows one to recover the global mass and linear momentum balance laws of the mixture. The model incorporates compressibility of the sediment and viscosity of the mixture through a viscous stress tensor. As a consequence of a dimensional analysis applied to the global mass conservation and linear momentum balance equations, the horizontal components of the compression term and the horizontal terms of the viscous stress tensor may be neglected. This results in a final model that is vertically consistent with the classical one-dimensional vertical model. Numerical simulations illustrate the coupled solids volume fraction and flow fields in various scenarios and the effect of the compressibility and viscosity terms. Various bottom topographies give rise to recirculation of the fluid and high solids volume fractions on the bottom.

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Acknowledgements

RB is supported by Fondecyt Project 1170473; CRHIAM, Project ANID/FONDAP/15130015; and CONICYT/PIA/Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal AFB170001. EDFN is supported by the Spanish Government and FEDER through the Research project MTM 2015-70490-C2-2-R. VO is supported by CONICYT scholarship.

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Authors and Affiliations

  1. CI2MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Raimund Bürger & Víctor Osores

  2. Departamento de Matemática Aplicada I, ETS Arquitectura, Universidad de Sevilla, Avda. Reina Mercedes No. 2, 41012, Sevilla, Spain

    Enrique D. Fernández-Nieto

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  1. Raimund Bürger
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  2. Enrique D. Fernández-Nieto
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  3. Víctor Osores
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Correspondence to Víctor Osores.

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Bürger, R., Fernández-Nieto, E.D. & Osores, V. A Multilayer Shallow Water Approach for Polydisperse Sedimentation with Sediment Compressibility and Mixture Viscosity. J Sci Comput 85, 49 (2020). https://doi.org/10.1007/s10915-020-01334-6

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  • DOI: https://doi.org/10.1007/s10915-020-01334-6

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