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A semi-implicit method for a degenerating convection-diffusion-reaction problem modeling secondary settling tanks

Acosta, Carlos D. ; Bürger, Raimund ; Careaga, Julio ; Diehl, Stefan LU ; Pineda, Romel and Támara, Daniel (2026) In Springer series 7.
Abstract
A one-dimensional model of reactive sedimentation in wastewater treatment is formulated. The model combines three main elements: the Activated Sludge Model No. 1 (ASM1) for the reactive part, a secondary sedimentation tank (SST) with a variable cross-sectional area, and a description with percentages of the solid phase. The final form of the model is a system of partial differential equations of the convection-diffusion-reaction type. Two new numerical methods are developed and compared for the proposed model, which differ in the discretization of the temporal variable. One method is explicit (method XPE) and the other is semi-implicit (method XPSI). In both cases, the Engquist-Osher numerical flux is used to approximate the nonlinear term... (More)
A one-dimensional model of reactive sedimentation in wastewater treatment is formulated. The model combines three main elements: the Activated Sludge Model No. 1 (ASM1) for the reactive part, a secondary sedimentation tank (SST) with a variable cross-sectional area, and a description with percentages of the solid phase. The final form of the model is a system of partial differential equations of the convection-diffusion-reaction type. Two new numerical methods are developed and compared for the proposed model, which differ in the discretization of the temporal variable. One method is explicit (method XPE) and the other is semi-implicit (method XPSI). In both cases, the Engquist-Osher numerical flux is used to approximate the nonlinear term of the convective flux of the solid particles. The numerical results demonstrate that the methods exhibit comparable accuracy in error estimation and that the semi-implicit scheme is more efficient.
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author
; ; ; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Advances in Nonlinear Hyperbolic Partial Differential Equations : ICIAM2023 - ICIAM2023
series title
Springer series
editor
Morales de Luna, T. and Morales de Luna, et. al.
volume
7
pages
36 pages
publisher
Springer
DOI
10.1007/978-981-96-9087-9_2
language
English
LU publication?
yes
id
ec770fa3-a505-456c-aea6-960c9d4c688a
date added to LUP
2026-06-03 10:25:56
date last changed
2026-06-08 16:32:31
@inbook{ec770fa3-a505-456c-aea6-960c9d4c688a,
  abstract     = {{A one-dimensional model of reactive sedimentation in wastewater treatment is formulated. The model combines three main elements: the Activated Sludge Model No. 1 (ASM1) for the reactive part, a secondary sedimentation tank (SST) with a variable cross-sectional area, and a description with percentages of the solid phase. The final form of the model is a system of partial differential equations of the convection-diffusion-reaction type. Two new numerical methods are developed and compared for the proposed model, which differ in the discretization of the temporal variable. One method is explicit (method XPE) and the other is semi-implicit (method XPSI). In both cases, the Engquist-Osher numerical flux is used to approximate the nonlinear term of the convective flux of the solid particles. The numerical results demonstrate that the methods exhibit comparable accuracy in error estimation and that the semi-implicit scheme is more efficient.<br/>}},
  author       = {{Acosta, Carlos D. and Bürger, Raimund and Careaga, Julio and Diehl, Stefan and Pineda, Romel and Támara, Daniel}},
  booktitle    = {{Advances in Nonlinear Hyperbolic Partial Differential Equations : ICIAM2023}},
  editor       = {{Morales de Luna, T. and Morales de Luna, et. al.}},
  language     = {{eng}},
  publisher    = {{Springer}},
  series       = {{Springer series}},
  title        = {{A semi-implicit method for a degenerating convection-diffusion-reaction problem modeling secondary settling tanks}},
  url          = {{http://dx.doi.org/10.1007/978-981-96-9087-9_2}},
  doi          = {{10.1007/978-981-96-9087-9_2}},
  volume       = {{7}},
  year         = {{2026}},
}