Numerical solution of a multi-class model for batch settling in water resource recovery facilities
(2017) In Applied Mathematical Modelling 49. p.415-436- Abstract
In Torfs et al. (2017) a new unified framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial differential equations (PDEs) modelling different settling unit processes in wastewater treatment such as primary and secondary settling tanks (PSTs and SSTs). The extension to a multi-class framework to deal with the distributed properties of the settling particles leads to a system of non-linear hyperbolic-parabolic PDEs whose solutions may contain very sharp transitions. This necessitates the use of a consistent and robust numerical method to obtain well-resolved and reliable approximations to the PDE solutions. The use of implicit–explicit Runge–Kutta (IMEX-RK) schemes, along with the... (More)
In Torfs et al. (2017) a new unified framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial differential equations (PDEs) modelling different settling unit processes in wastewater treatment such as primary and secondary settling tanks (PSTs and SSTs). The extension to a multi-class framework to deal with the distributed properties of the settling particles leads to a system of non-linear hyperbolic-parabolic PDEs whose solutions may contain very sharp transitions. This necessitates the use of a consistent and robust numerical method to obtain well-resolved and reliable approximations to the PDE solutions. The use of implicit–explicit Runge–Kutta (IMEX-RK) schemes, along with the weighted essentially non-oscillatory (WENO) shock-capturing technology for the discretization of the set of equations, is advocated in this work. The versatility of the proposed unified framework is demonstrated through a set of numerical examples for batch settling occurring in both PSTs and SSTs, along with the efficiency and reliability of the numerical scheme.
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- author
- Bürger, Raimund ; Diehl, Stefan LU ; Martí, M. Carmen ; Mulet, Pep ; Nopens, Ingmar ; Torfs, Elena and Vanrolleghem, Peter A
- organization
- publishing date
- 2017-09-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Convection–diffusion equation, Implicit–explicit Runge–Kutta scheme, Multi-class kinematic flow model, Settling velocity distribution, Wastewater treatment
- in
- Applied Mathematical Modelling
- volume
- 49
- pages
- 22 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85020622810
- wos:000404823100024
- ISSN
- 0307-904X
- DOI
- 10.1016/j.apm.2017.05.014
- language
- English
- LU publication?
- yes
- id
- bb073d2b-7554-41a6-aa4d-4415c00f4666
- date added to LUP
- 2017-07-04 07:57:19
- date last changed
- 2025-01-07 16:35:09
@article{bb073d2b-7554-41a6-aa4d-4415c00f4666,
abstract = {{<p>In Torfs et al. (2017) a new unified framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial differential equations (PDEs) modelling different settling unit processes in wastewater treatment such as primary and secondary settling tanks (PSTs and SSTs). The extension to a multi-class framework to deal with the distributed properties of the settling particles leads to a system of non-linear hyperbolic-parabolic PDEs whose solutions may contain very sharp transitions. This necessitates the use of a consistent and robust numerical method to obtain well-resolved and reliable approximations to the PDE solutions. The use of implicit–explicit Runge–Kutta (IMEX-RK) schemes, along with the weighted essentially non-oscillatory (WENO) shock-capturing technology for the discretization of the set of equations, is advocated in this work. The versatility of the proposed unified framework is demonstrated through a set of numerical examples for batch settling occurring in both PSTs and SSTs, along with the efficiency and reliability of the numerical scheme.</p>}},
author = {{Bürger, Raimund and Diehl, Stefan and Martí, M. Carmen and Mulet, Pep and Nopens, Ingmar and Torfs, Elena and Vanrolleghem, Peter A}},
issn = {{0307-904X}},
keywords = {{Convection–diffusion equation; Implicit–explicit Runge–Kutta scheme; Multi-class kinematic flow model; Settling velocity distribution; Wastewater treatment}},
language = {{eng}},
month = {{09}},
pages = {{415--436}},
publisher = {{Elsevier}},
series = {{Applied Mathematical Modelling}},
title = {{Numerical solution of a multi-class model for batch settling in water resource recovery facilities}},
url = {{http://dx.doi.org/10.1016/j.apm.2017.05.014}},
doi = {{10.1016/j.apm.2017.05.014}},
volume = {{49}},
year = {{2017}},
}