A dynamic multilayer shallow water model for polydisperse sedimentation

A multilayer shallow water approach for the approximate description of polydisperse sedimentation in a viscous fluid is presented. The fluid is assumed to carry finely dispersed solid particles that belong to a finite number of species that differ in density and size. These species segregate and for...

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Autores: Bürger, Raimund, Fernández Nieto, Enrique Domingo, Osores Escalona, Víctor
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/161701
Acceso en línea:https://hdl.handle.net/11441/161701
https://doi.org/10.1051/m2an/2019032
Access Level:acceso abierto
Palabra clave:Multilayer shallow water model
Polydisperse sedimentation
Path-conservative method
Viscous flow
Recirculation
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spelling A dynamic multilayer shallow water model for polydisperse sedimentationBürger, RaimundFernández Nieto, Enrique DomingoOsores Escalona, VíctorMultilayer shallow water modelPolydisperse sedimentationPath-conservative methodViscous flowRecirculationA multilayer shallow water approach for the approximate description of polydisperse sedimentation in a viscous fluid is presented. The fluid is assumed to carry finely dispersed solid particles that belong to a finite number of species that differ in density and size. These species segregate and form areas of different composition. In addition, the settling of particles influences the motion of the ambient fluid. A distinct feature of the new approach is the particular definition of the average velocity of the mixture. It takes into account the densities of the solid particles and the fluid and allows us to recover the global mass conservation and linear momentum balance laws of the mixture. This definition motivates a modification of the Masliyah–Lockett–Bassoon (MLB) settling velocities of each species. The multilayer shallow water model allows one to determine the spatial distribution of the solid particles, the velocity field, and the evolution of the free surface of the mixture. The final model can be written as a multilayer model with variable density where the unknowns are the average velocities and concentrations in each layer, the transfer terms across each interface, and the total mass. An explicit formula of the transfer terms leads to a reduced form of the system. Finally, an explicit bound of the minimum and maximum eigenvalues of the transport matrix of the system is utilized to design a Harten–Lax–van Leer (HLL)-type path-conservative numerical method. Numerical simulations illustrate the coupled polydisperse sedimentation and flow fields in various scenarios, including sedimentation in a type of basin that is used in practice in mining industry and in a basin whose bottom topography gives rise to recirculations of the fluid and high solids concentrations.EDP SciencesMatemática Aplicada IFQM120: Modelado Matemático y Simulación de Sistemas MedioambientalesFondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT). ChileGobierno de EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/161701https://doi.org/10.1051/m2an/2019032reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésESAIM: Mathematical Modelling and Numerical Analysis, 53 (4), 1391-1432.1170473MTM 2015-70490-C2-2-Rhttps://www.esaim-m2an.org/articles/m2an/pdf/2019/04/m2an180072.pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1617012026-06-17T12:51:07Z
dc.title.none.fl_str_mv A dynamic multilayer shallow water model for polydisperse sedimentation
title A dynamic multilayer shallow water model for polydisperse sedimentation
spellingShingle A dynamic multilayer shallow water model for polydisperse sedimentation
Bürger, Raimund
Multilayer shallow water model
Polydisperse sedimentation
Path-conservative method
Viscous flow
Recirculation
title_short A dynamic multilayer shallow water model for polydisperse sedimentation
title_full A dynamic multilayer shallow water model for polydisperse sedimentation
title_fullStr A dynamic multilayer shallow water model for polydisperse sedimentation
title_full_unstemmed A dynamic multilayer shallow water model for polydisperse sedimentation
title_sort A dynamic multilayer shallow water model for polydisperse sedimentation
dc.creator.none.fl_str_mv Bürger, Raimund
Fernández Nieto, Enrique Domingo
Osores Escalona, Víctor
author Bürger, Raimund
author_facet Bürger, Raimund
Fernández Nieto, Enrique Domingo
Osores Escalona, Víctor
author_role author
author2 Fernández Nieto, Enrique Domingo
Osores Escalona, Víctor
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT). Chile
Gobierno de España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
dc.subject.none.fl_str_mv Multilayer shallow water model
Polydisperse sedimentation
Path-conservative method
Viscous flow
Recirculation
topic Multilayer shallow water model
Polydisperse sedimentation
Path-conservative method
Viscous flow
Recirculation
description A multilayer shallow water approach for the approximate description of polydisperse sedimentation in a viscous fluid is presented. The fluid is assumed to carry finely dispersed solid particles that belong to a finite number of species that differ in density and size. These species segregate and form areas of different composition. In addition, the settling of particles influences the motion of the ambient fluid. A distinct feature of the new approach is the particular definition of the average velocity of the mixture. It takes into account the densities of the solid particles and the fluid and allows us to recover the global mass conservation and linear momentum balance laws of the mixture. This definition motivates a modification of the Masliyah–Lockett–Bassoon (MLB) settling velocities of each species. The multilayer shallow water model allows one to determine the spatial distribution of the solid particles, the velocity field, and the evolution of the free surface of the mixture. The final model can be written as a multilayer model with variable density where the unknowns are the average velocities and concentrations in each layer, the transfer terms across each interface, and the total mass. An explicit formula of the transfer terms leads to a reduced form of the system. Finally, an explicit bound of the minimum and maximum eigenvalues of the transport matrix of the system is utilized to design a Harten–Lax–van Leer (HLL)-type path-conservative numerical method. Numerical simulations illustrate the coupled polydisperse sedimentation and flow fields in various scenarios, including sedimentation in a type of basin that is used in practice in mining industry and in a basin whose bottom topography gives rise to recirculations of the fluid and high solids concentrations.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/161701
https://doi.org/10.1051/m2an/2019032
url https://hdl.handle.net/11441/161701
https://doi.org/10.1051/m2an/2019032
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv ESAIM: Mathematical Modelling and Numerical Analysis, 53 (4), 1391-1432.
1170473
MTM 2015-70490-C2-2-R
https://www.esaim-m2an.org/articles/m2an/pdf/2019/04/m2an180072.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv EDP Sciences
publisher.none.fl_str_mv EDP Sciences
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812455

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