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A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation

Bürger, Raimund ; Diehl, Stefan LU and Mejías, Camilo (2018) In ESAIM: Mathematical Modelling and Numerical Analysis 52(2). p.365-392
Abstract

Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the underlying strongly degenerate parabolic, nonlinear model partial differential equation (PDE). Such a model is extended to describe the sedimentation of multi-component particles that react with several soluble components of the liquid phase. The fundamental balance equations contain the mass percentages of the components of the solid and liquid phases. The equations are reformulated as a system of nonlinear PDEs that can be solved consecutively... (More)

Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the underlying strongly degenerate parabolic, nonlinear model partial differential equation (PDE). Such a model is extended to describe the sedimentation of multi-component particles that react with several soluble components of the liquid phase. The fundamental balance equations contain the mass percentages of the components of the solid and liquid phases. The equations are reformulated as a system of nonlinear PDEs that can be solved consecutively in each time step by an explicit numerical scheme. This scheme combines a difference scheme for conservation laws with discontinuous ux with an approach of numerical percentage propagation for multi-component ows. The main result is an invariant-region property, which implies that physically relevant numerical solutions are produced. Simulations of denitrification in secondary settling tanks in wastewater treatment illustrate the model and its discretization.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Clarifier-thickener, Invariant-region property, Multi-component ow, Percentage propagation, Wastewater treatment
in
ESAIM: Mathematical Modelling and Numerical Analysis
volume
52
issue
2
pages
28 pages
publisher
EDP Sciences
external identifiers
  • scopus:85053723937
ISSN
0764-583X
DOI
10.1051/m2an/2017038
language
English
LU publication?
yes
id
acc97220-6152-4da5-b52f-85195acdf143
date added to LUP
2018-10-19 12:34:01
date last changed
2020-01-13 01:04:36
@article{acc97220-6152-4da5-b52f-85195acdf143,
  abstract     = {<p>Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the underlying strongly degenerate parabolic, nonlinear model partial differential equation (PDE). Such a model is extended to describe the sedimentation of multi-component particles that react with several soluble components of the liquid phase. The fundamental balance equations contain the mass percentages of the components of the solid and liquid phases. The equations are reformulated as a system of nonlinear PDEs that can be solved consecutively in each time step by an explicit numerical scheme. This scheme combines a difference scheme for conservation laws with discontinuous ux with an approach of numerical percentage propagation for multi-component ows. The main result is an invariant-region property, which implies that physically relevant numerical solutions are produced. Simulations of denitrification in secondary settling tanks in wastewater treatment illustrate the model and its discretization.</p>},
  author       = {Bürger, Raimund and Diehl, Stefan and Mejías, Camilo},
  issn         = {0764-583X},
  language     = {eng},
  number       = {2},
  pages        = {365--392},
  publisher    = {EDP Sciences},
  series       = {ESAIM: Mathematical Modelling and Numerical Analysis},
  title        = {A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation},
  url          = {http://dx.doi.org/10.1051/m2an/2017038},
  doi          = {10.1051/m2an/2017038},
  volume       = {52},
  year         = {2018},
}