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An invariant-region-preserving scheme for a convection-reaction-Cahn–Hilliard multiphase model of biofilm growth in slow sand filters

Careaga, Julio LU ; Diehl, Stefan LU and Manríquez, Jaime LU orcid (2026) In Computers and Mathematics with Applications 201. p.146-170
Abstract

A multidimensional model of biofilm growth present in the supernatant water of a Slow Sand Filter is derived. The multiphase model, consisting of solid and liquid phases, is written as a convection-reaction system with a Cahn–Hilliard-type equation with degenerate mobility coupled to a Stokes-flow equation for the mixture velocity. An upwind discontinuous Galerkin approach is used to approximate the convection-reaction equations, whereas an H 1 -conforming primal formulation is proposed for the Stokes system. By means of a splitting procedure due to the reaction terms, an invariant-region principle is shown for the concentration unknowns, namely non-negativity for all phases and an upper bound for the total concentration of the solid... (More)

A multidimensional model of biofilm growth present in the supernatant water of a Slow Sand Filter is derived. The multiphase model, consisting of solid and liquid phases, is written as a convection-reaction system with a Cahn–Hilliard-type equation with degenerate mobility coupled to a Stokes-flow equation for the mixture velocity. An upwind discontinuous Galerkin approach is used to approximate the convection-reaction equations, whereas an H 1 -conforming primal formulation is proposed for the Stokes system. By means of a splitting procedure due to the reaction terms, an invariant-region principle is shown for the concentration unknowns, namely non-negativity for all phases and an upper bound for the total concentration of the solid phases. Numerical examples with reduced biofilm reactions are presented to illustrate the performance of the model and numerical scheme.

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author
; and
organization
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type
Contribution to journal
publication status
published
subject
keywords
Biofilm growth, Cahn–Hilliard–Stokes equations, Discontinuous Galerkin, Positivity preserving, Slow sand filtration, Upwind scheme
in
Computers and Mathematics with Applications
volume
201
pages
25 pages
publisher
Elsevier
external identifiers
  • scopus:105020939012
ISSN
0898-1221
DOI
10.1016/j.camwa.2025.10.012
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 The Author(s).
id
5478c59f-20b8-4fc3-a9b6-63fb6d54f246
date added to LUP
2026-04-21 12:01:15
date last changed
2026-08-17 12:01:12
@article{5478c59f-20b8-4fc3-a9b6-63fb6d54f246,
  abstract     = {{<p>A multidimensional model of biofilm growth present in the supernatant water of a Slow Sand Filter is derived. The multiphase model, consisting of solid and liquid phases, is written as a convection-reaction system with a Cahn–Hilliard-type equation with degenerate mobility coupled to a Stokes-flow equation for the mixture velocity. An upwind discontinuous Galerkin approach is used to approximate the convection-reaction equations, whereas an  H 1 -conforming primal formulation is proposed for the Stokes system. By means of a splitting procedure due to the reaction terms, an invariant-region principle is shown for the concentration unknowns, namely non-negativity for all phases and an upper bound for the total concentration of the solid phases. Numerical examples with reduced biofilm reactions are presented to illustrate the performance of the model and numerical scheme.</p>}},
  author       = {{Careaga, Julio and Diehl, Stefan and Manríquez, Jaime}},
  issn         = {{0898-1221}},
  keywords     = {{Biofilm growth; Cahn–Hilliard–Stokes equations; Discontinuous Galerkin; Positivity preserving; Slow sand filtration; Upwind scheme}},
  language     = {{eng}},
  month        = {{01}},
  pages        = {{146--170}},
  publisher    = {{Elsevier}},
  series       = {{Computers and Mathematics with Applications}},
  title        = {{An invariant-region-preserving scheme for a convection-reaction-Cahn–Hilliard multiphase model of biofilm growth in slow sand filters}},
  url          = {{http://dx.doi.org/10.1016/j.camwa.2025.10.012}},
  doi          = {{10.1016/j.camwa.2025.10.012}},
  volume       = {{201}},
  year         = {{2026}},
}