A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation
(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.
(Less)
- author
- Bürger, Raimund ; Diehl, Stefan LU and Mejías, Camilo
- organization
- publishing date
- 2018
- 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
- 2022-03-17 18:20:16
@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}},
keywords = {{Clarifier-thickener; Invariant-region property; Multi-component ow; Percentage propagation; Wastewater treatment}},
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}},
}