On numerical methods for hyperbolic conservation laws and related equations modelling sedimentation of solid-liquid suspensions

F. Betancourt, Raimund Bürger, R. Ruiz-Baier, H. Torres, C. A. Vega

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

5 Citations (Scopus)

Abstract

A classical kinematical model of sedimentation of small equal-sized particles dispersed in a viscous fluid leads to a scalar conservation law with a nonlinear flux. Several extensions of this model are reviewed, with a strong focus on recently developed numerical methods. These extensions include a one-dimensional clarifier-thickener model giving rise to a conservation law with discontinuous flux, a conservation law with nonlocal flux, systems of nonlinear conservation modelling the sedimentation of polydisperse suspensions, and sedimentation-flow models consisting of a conservation law coupled with the Stokes or Navier-Stokes system in two space dimensions. Numerical examples are presented.

Original languageEnglish
Title of host publicationHyperbolic Conservation Laws and Related Analysis with Applications
EditorsGui-Qiang G Chen, Helge Holden, Kenneth H Karlsen
Place of PublicationHeidelberg Germany
PublisherSpringer
Pages23-68
Number of pages46
Volume49
ISBN (Electronic)978-3-642-39007-4
ISBN (Print)9783642390067
DOIs
Publication statusPublished - 7 Feb 2014
Externally publishedYes
EventWorkshop on Hyperbolic Conservation Laws and Related Analysis with Applications - Edinburgh, United Kingdom
Duration: 19 Sep 201123 Sep 2011

Publication series

NameSpringer Proceedings in Mathematics and Statistics
PublisherSpringer
Volume49
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceWorkshop on Hyperbolic Conservation Laws and Related Analysis with Applications
CountryUnited Kingdom
CityEdinburgh
Period19/09/1123/09/11

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