An invariant-region-preserving scheme for a convection-reaction-Cahn-Hilliard multiphase model of biofilm growth in slow sand filters
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915231717916672 |
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| author | Careaga, Julio Diehl, Stefan Manríquez, Jaime |
| author_facet | Careaga, Julio Diehl, Stefan Manríquez, Jaime |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An invariant-region-preserving scheme for a convection-reaction-Cahn-Hilliard multiphase model of biofilm growth in slow sand filters Careaga, Julio Diehl, Stefan Manríquez, Jaime Numerical Analysis 35Q49, 76T20, 35Q92 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. |
| title | An invariant-region-preserving scheme for a convection-reaction-Cahn-Hilliard multiphase model of biofilm growth in slow sand filters |
| topic | Numerical Analysis 35Q49, 76T20, 35Q92 |
| url | https://arxiv.org/abs/2504.04852 |