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Numerical solution of a multi-class model for batch settling in water resource recovery facilities

Bürger, Raimund; Diehl, Stefan LU ; Martí, M. Carmen; Mulet, Pep; Nopens, Ingmar; Torfs, Elena and Vanrolleghem, Peter A (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
organization
publishing date
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 Inc.
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
2018-05-29 12:06:55
@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},
  keyword      = {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 Inc.},
  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},
  volume       = {49},
  year         = {2017},
}